straight lines dpp -11th elite
TRANSCRIPT
Straight Lines DPP- 11th Elite
Q1. The vertices of a triangle ABC are A(-2, 3), B(2, -1) and C(4, 0). Find cos A.
Q2. Prove that the points (-4, -1), (-2, -4), (4, 0) and (2, 3) are the vertices of a rectangle.
Q3. Find the coordinates of the points which trisect the line segment joining (1, -2) and (-3, 4)
Q4. Find the ratio in which the segment joining the points A(2, -4) and B(4, 5) is divided by the X-axis.
Q5. Find the ratio in which the segment joining the points A(2, -4) and B(4, 5) is divided by x + y - 1 = 0
Q6. Find the ratio in which the segment joining the points A(2, -4) and B(4, 5) is divided by 2x + y + 1 = 0.
Q7. The coordinates of the midpoints of the sides of a triangle are (1, 1), (3, 2) and (4, 1). Find the coordinates of its vertices.
Q8. Determine the ratio in which the line 3x + y - 9 = 0 divide the segment joining the points (1, 3) and (2, 7).
Q9. If the midpoints of a triangle are (2, 0), (2, 1) and (0, 1) then find coordinates of its vertices.
Q10. Find the orthocentre of the triangle whose vertices are (0, 0), (3, 0) and (0, 4).
Q11. If the circumcentre of an acute angled triangle lies at the origin and the centroid is the middle point of the line joining the points (a2 + 1, a2 + 1) and(2a, -2a), then find the orthocentre.
Q12. Two vertices of a triangle are (5, -1) and (-2, 3). If the orthocentre of the triangle is the origin, then coordinates of third vertex are
(4, 7)
(-4, 7)
(-4, -7)
None of these
A
B
C
D
Q13. Two vertices of a ΔABC are A(0, 0), B(0, 2) and C(2, 0). Find the distance between the circumcentre and orthocentre.
Q14. Orthocentre and circumcentre of a ΔABC are (a, b) and (c, d), respectively. If the coordinates of the vertex A are (x
1, y
1), then find the coordinates of the
middle point of BC.
Q15. If the coordinates of two points A and B are (3, 4) and (5, -2), respectively. Find the coordinates of any point P if PA = PB and area of ΔPAB = 10 sq. units.
Q16. If ⍺, β, γ are the roots of the equation x3 - 3px2 + 3qx - 1 = 0, then find the centroid of the triangle whose vertices are (⍺, β + γ), (β, ⍺ + γ), (γ, ⍺ + β)
Q17. Find the area of a triangle whose vertices are (t, t + 2), (t + 3, t) and (t + 2, t + 2)
Q18. Find the area of a pentagon whose vertices are (4, 3), (-5, 6) (0, 7), (3, -6) and (-7, -2)
Q19. Find the value of k if (k + 1, 2 - k), (1 - k, - k) and (2 + k, 3 - k) are collinear.
Q20. Prove that the points (a, b + c), (b, c + a) and (c, a + b) are collinear.
Q21. The locus of a point which moves such that its distance from the point(0, 0) is twice its distance from the y-axis, is
x2 - y2 = 0
3x2 - y2 = 0
x2 - 3y2 = 0
None of these
A
B
C
D
Q22. Find the locus of a point whose coordinates are given by x = 2t3 + t, y = t - 1, where t is a parameter
Q23. Find the locus of a movable point P, for which the sum of its distance from (0, 3) and (0, -3) is 8.
Q24. If P be the mid-point of the straight line joining the points A(1, 2) and Q where Q is a variable point on the curve x2 + y2 + x + y = 0. Find the locus of P.
Q25. Find the locus of a point such that the sum of its distance from the points (0, 2) and (0, -2) is 6.
Q26. Find the equation of the curve 2x2 + y2 - 3x + 5y - 8 = 0, when the origin is shifted to the point (-1, 2) without changing the direction of the axes.
Q27. The equation of a curve referred to the new axes retaining their directions and origin is (4, 5) is x2 + y2 = 36. Find the equation referred to the original axes.
Q28. Find the equation to which the equation x2 + 7xy - 2y2 + 17x - 26y - 60 = 0 is transformed if the origin is shifted to the point (2, -3), the axes remaining parallel to the original axis.
Q29. Find the equation of a line which passes through the point (2, 3) and whose x-intercept is twice of y-intercept.
Q30. Shift the origin to a suitable point so that the equation y2 +4y + 8x - 2 = 0 will not contain term in y and constant term.
Q31. Determine x so that the line passing through (3, 4) and (x, 5) makes 135° angle with the positive direction of x-axis.
Q32. Find the equation of a line passing through the point (3, 2) and cuts off intercepts a and b on x- and y-axes such that a - b = 2.
Q33. Find the equation of the straight line that passes through the point (3, 4) and perpendicular to the line 3x + 2y + 5 = 0.
Q34. If the straight line, 2x - 3y + 17 = 0 is perpendicular to the line passing through the points (7, 17) and (15, β), then β equals
5
-5
JEE Main - 2019A
B
C
D
Q35. Find the equation of the straight line which passes through the origin and makes angle 60° with the line
Q36. A line intersects the straight lines 5x - y - 4 = 0 and 3x - 4y - 4 = 0 atA and B, respectively. If a point P(1, 5) on the line AB is such that AP : PB = 2 : 1 (internally), find point A.
Q37. If the foot of the perpendicular from the origin to a straight line is at the point (3, -4). Then find the equation of the line.
Q38. Find the equation of a straight line which makes an angle of
with the positive direction of x-axis and cuts an intercept of 6 units in the negative direction of y-axis.
Q39. A line passes through the point A(2, 0) which makes an angle of 30° with the positive direction of x-axis and is rotated about A in clockwise direction through an angle of 15°. Find the equation of the straight line in the new position.
Q40. The line joining the points A(2, 0) and B(3, 1) is rotated about A in the anti-clockwise direction through an angle of 15°. Find the equation of a line in the new position.
Q41. Convert the following equation of a line into normal form. 3x + 4y + 5
Q42. Reduce into the (i) slope intercept form and also find its slope and y-intercept.(ii) intercept form and also find the lengths of x and y intercepts.(iii) normal form and also find the values of p and ⍺.
Q43. In what ratio does the line joining the points (2, 3) and (4, 1) divide the segment joining the points (1, 2) and (4, 3)?
Q44. If the straight line, 2x - 3y + 17 = 0 is perpendicular to the line passing through the points(7, 17) and (15, β), then β equals
5
-5
JEE Main - 2019A
B
C
D
Q45. Find the measure of the∠ ABC if the coordinates of A, B and C are A(-2, 1), B(2, 3) and C(-2, -4).
Q46. Find the equation of a line through (1, 2) that is perpendicular to the line x - 2y + 1 = 0.
x + 2y - 4 = 0
x - 2y - 4 = 0
2x + y - 4 = 0
2x - y - 4 = 0
A
B
C
D
Q47. The equation of straight line cutting off an intercept -2 from y-axis and being equally inclined to the axes are
y = x + 2, y = x - 2
y = x - 2, y = x - 2
y = -x - 2, y = x - 2
None of these
A
B
C
D
tan-1(7)
Q48. The angle between the line x + y = 3 and the line joining the points (1, 1) and (-3, 4) is
None of these
A
B
C
D
Q49. Find the angle between the lines
None of these
A
B
C
D
Q50. Find angles between the lines
35°
45°
30°
60°
A
B
C
D
Q51. The triangle formed by the lines x + y = 0, 3x + y = 4, x + 3y = 4 is
Isosceles
Right angled
Equilateral
None of these
A
B
C
D
Q52. Two lines are drawn trough (3, 4) each of which makes angle of 45° with line x - y = 2, then area of the triangle formed by these lines is
9 sq units
2 sq units
A
B
C
D
Q53. The inclination of the straight line passing through the point (-3, 6) and the mid-point of the line joining the points (4, -5) and (-2, 9) is
A
B
C
D
Q54. The equations of the lines through (1, 2) which make equal angles with
x = 1, y = 2
x = 2, y = 1
A
B
C
D
Q55. Find the equations of the lines through the line makes an angle 45° with the line x - 2y = 3.
Q56. A vertex of an equilateral triangle is (2, 3) and the equation of the opposite side x + y = 2. Find the equation of the other sides of the triangle.
Q57. A line 4x + y = 1 through the point A(2, -7) meets the line BC, whose equation is 3x - 4y + 1 = 0 at the point B. Find the equation of the line AC so that AB = AC.
Q58. Find the equations of straight lines passing through (-2, -7) and having an intercept of length 3 between the straight lines 4x + 3y = 12 and 4x + 3y = 3.
Q59. Find the equations of the lines passing through the point (2, 3) and equally inclined to the lines 3x - 4y = 7 and 12x - 5y + 6 = 0.
Q60. In triangle ABC, equation of the right bisectors of the sides AB and AC arex + y = 0 and y - x = 0 respectively. If A = (5, 7) then find the equation of side BC.
Q61. The coordinates of the foot of perpendicular from the point (2, 3) on the line y = 3x + 4 is given by
A
B
C
D
(1, -1)
Q62. A point equidistant from the lines 4x + 3y + 10 = 0, 5x - 12y + 26 = 0 and 7x + 24y - 50 = 0 is
(0, 0)
(1, 1)
(0, 1)
A
B
C
D
Q63. Find the image of the point (4, -13) in the line 5x + y + 6 = 0.
Q64. Find the foot of the perpendicular from the point (2, 4) upon x + y = 1.
Q65. The distance of the point of intersection of lines 2x - 3y + 5 = 0 and3x + 4y = 0 from the line 5x - 2y = 0 is
A
B
C
D
Q66. The length of perpendicular from the point (a cos ⍺, a si ⍺) upon the straight line y = x tan ⍺ + c, c > 0, is
c
c cos ⍺
c sin2 ⍺
c sec2 ⍺
A
B
C
D
Q67. Equation of the line passing through (1, 2) and parallel to the line y = 3x - 1 is
y + 2 = x + 1
y - 2 = 3(x - 1)
y + 2 = 3(x + 1)
y - 2 = x - 1
A
B
C
D
Q68. The distance of the point (3, 5) from the line 2x + 3y - 14 = 0 measured parallel to line x - 2y = 1, is
A
B
C
D
Q69. Find the image of the point (3, 4) with respect to the line y = x.
Q70. Area of parallelogram whose sides are 2x + y + 1 = 0, 2x + y + 4 = 0,x - 3y - 1 = 0 and x - 3y + 2 = 0 is equal to______.
A
B
C
D
Q71. If t1 and t
2 are roots of the equation t2 + λt + 1 = 0, where λ is an arbitrary
constant. Then, the line joining the points (at1
2, 2 at1) and (at
22 , 2 at
2 ) always
passes through a fixed point whose coordinates are
(a, 0)
(0, a)
(-a, 0)
(0, -a)
A
B
C
D
Q72. The point moves such that the area of the triangle formed by it with the points (1, 5) and (3, -7) is 21 sq units. The locus of the point is
6x + y - 32 = 0
x + 6y - 32 = 0
6x - y + 32 = 0
6x - y - 32 = 0
A
B
C
D
Q73. The equations of the respective perpendicular bisectors of sides AB and AC of a Δ ABC are x − y + 5 = 0 and x + 2y = 0. If the coordinates of A are (1, –2), then find the equation of BC.
Q74. A ray of light is sent along the line x - 2y = 3. Upon reaching the line3x - 2y = 5, the ray is reflected from it. Find the equation of the line containing the reflected ray.
Q75. A ray of light passing through the point (1, 2) is reflected on the x-axis at a point P and passes through the point (5, 3). Find the abscissa of the point P.
Q76. Find equation of straight lines passing through (2, 3) and having an intercept of length 2 units between 2x + y = 3 and 2x + y = 5.
Q77. Equation of diagonals of the square formed by the lines x = 0, y = 0, x = 1 and y = 1 are
y = x, y + x = 1
y = x, y + x = 2
y = 2x, y + 2x = 1
A
B
C
D
Q78. Consider the family of lines 5x + 3y - 2 + λ1 (3x - y - 4) = 0 and
x - y + 1 + λ2(2x - y - 2) = 0. Find the equation of a straight line that belongs to
both the families.
Q79. Lines 2x + y = 1 and 2x + y = 7 are
on the same side of a point
same lines
on the opposite side of a point
perpendicular lines
A
B
C
D
Q80. Find the equation of a line which passes through the intersection point of the lines 3x − 4y + 6 = 0 and x + y + 2 = 0, that is farthest from the point P (2, 3).
Q81. The equations of perpendicular bisectors of sides AB and AC of a ΔABC are x - y + 5 = 0 and x + 2y = 0 respectively. If the coordinates of vertex A are (1, -2), then the equation of BC is
23x + 14y - 40 = 0
23x - 14y + 40 = 0
14x - 23y + 40 = 0
14x + 23y - 40 = 0
A
B
C
D
Q82. The equations of the bisector of the acute angle between the lines3x - 4y + 7 = 0 and 12x + 5y - 2 = 0 is
99x - 27y - 81 = 0
21x + 77y - 101 = 0
11x - 3y + 9 = 0
21x + 77y + 101 = 0
A
B
C
D
Q83. The equations of bisectors of the angle between the lines |x| = |y| are
y = ±x and x = 0
y = 0 and x = 0
None of these
A
B
C
D
Q84. Find the equation of the bisectors bisecting the angle containing the origin of the straight lines 4x + 3y = 6 and 5x + 12y + 9 = 0.
Q85. Find the bisector of the acute angle between the lines x + y = 3 and 7x - y + 5 = 0.
Q86. Prove that the length of the perpendicular drawn from any point of the line 7x - 9y + 10 = 0 to the lines 3x + 4y = 5 and 12x + 5y = 7 are the same.
Straight Lines DPP- 11th Elite Solutions
Q1. The vertices of a triangle ABC are A(-2, 3), B(2, -1) and C(4, 0). Find cos A.
Solution:
Q2. Prove that the points (-4, -1), (-2, -4), (4, 0) and (2, 3) are the vertices of a rectangle.
Solution:
Q3. Find the coordinates of the points which trisect the line segment joining (1, -2) and (-3, 4)
Solution:
Q4. Find the ratio in which the segment joining the points A(2, -4) and B(4, 5) is divided by the X-axis.
Solution:
Q5. Find the ratio in which the segment joining the points A(2, -4) and B(4, 5) is divided by x + y - 1 = 0
Solution:
Q6. Find the ratio in which the segment joining the points A(2, -4) and B(4, 5) is divided by 2x + y + 1 = 0.
Solution:
Q7. The coordinates of the midpoints of the sides of a triangle are (1, 1), (3, 2) and (4, 1). Find the coordinates of its vertices.
Solution:
Q8. Determine the ratio in which the line 3x + y - 9 = 0 divide the segment joining the points (1, 3) and (2, 7).
Solution:
Q9. If the midpoints of a triangle are (2, 0), (2, 1) and (0, 1) then find coordinates of its vertices.
P (2, 0)
A (x1, y1)
B (x2, y2) C (x3, y3)Q (2, 1)
R (0, 1)
Solution:
Solution:
Alternate Solution
O
Q (2, 1)(0, 2)
R (0, 1)
P(2, 0) (4, 0)X
Y
Solution:
Q10. Find the orthocentre of the triangle whose vertices are (0, 0), (3, 0) and (0, 4).
Solution:
Q11. If the circumcentre of an acute angled triangle lies at the origin and the centroid is the middle point of the line joining the points (a2 + 1, a2 + 1) and(2a, -2a), then find the orthocentre.
Solution:
Q12. Two vertices of a triangle are (5, -1) and (-2, 3). If the orthocentre of the triangle is the origin, then coordinates of third vertex are
(4, 7)
(-4, 7)
(-4, -7)
None of these
A
B
C
D
Solution:
Q13. Two vertices of a ΔABC are A(0, 0), B(0, 2) and C(2, 0). Find the distance between the circumcentre and orthocentre.
Solution:
Q14. Orthocentre and circumcentre of a ΔABC are (a, b) and (c, d), respectively. If the coordinates of the vertex A are (x
1, y
1), then find the coordinates of the
middle point of BC.
Solution:
Q15. If the coordinates of two points A and B are (3, 4) and (5, -2), respectively. Find the coordinates of any point P if PA = PB and area of ΔPAB = 10 sq. units.
Solution:
Solution:
Q16. If ⍺, β, γ are the roots of the equation x3 - 3px2 + 3qx - 1 = 0, then find the centroid of the triangle whose vertices are (⍺, β + γ), (β, ⍺ + γ), (γ, ⍺ + β)
Solution:
Q17. Find the area of a triangle whose vertices are (t, t + 2), (t + 3, t) and (t + 2, t + 2)
Solution:
Q18. Find the area of a pentagon whose vertices are (4, 3), (-5, 6) (0, 7), (3, -6) and (-7, -2)
Solution:
Q19. Find the value of k if (k + 1, 2 - k), (1 - k, - k) and (2 + k, 3 - k) are collinear.
Solution:
Q20. Prove that the points (a, b + c), (b, c + a) and (c, a + b) are collinear.
Solution:
Q21. The locus of a point which moves such that its distance from the point(0, 0) is twice its distance from the y-axis, is
x2 - y2 = 0
3x2 - y2 = 0
x2 - 3y2 = 0
None of these
A
B
C
D
Solution:
Q22. Find the locus of a point whose coordinates are given by x = 2t3 + t, y = t - 1, where t is a parameter
Solution:
Q23. Find the locus of a movable point P, for which the sum of its distance from (0, 3) and (0, -3) is 8.
Solution:
Solution:
Q24. If P be the mid-point of the straight line joining the points A(1, 2) and Q where Q is a variable point on the curve x2 + y2 + x + y = 0. Find the locus of P.
Solution:
Solution:
Q25. Find the locus of a point such that the sum of its distance from the points (0, 2) and (0, -2) is 6.
Solution:
Q26. Find the equation of the curve 2x2 + y2 - 3x + 5y - 8 = 0, when the origin is shifted to the point (-1, 2) without changing the direction of the axes.
Solution:
Q27. The equation of a curve referred to the new axes retaining their directions and origin is (4, 5) is x2 + y2 = 36. Find the equation referred to the original axes.
Solution:
Q28. Find the equation to which the equation x2 + 7xy - 2y2 + 17x - 26y - 60 = 0 is transformed if the origin is shifted to the point (2, -3), the axes remaining parallel to the original axis.
Solution:
Q29. Find the equation of a line which passes through the point (2, 3) and whose x-intercept is twice of y-intercept.
Solution:
Q30. Shift the origin to a suitable point so that the equation y2 +4y + 8x - 2 = 0 will not contain term in y and constant term.
Solution:
Q31. Determine x so that the line passing through (3, 4) and (x, 5) makes 135° angle with the positive direction of x-axis.
Solution:
Q32. Find the equation of a line passing through the point (3, 2) and cuts off intercepts a and b on x- and y-axes such that a - b = 2.
Solution:
Q33. Find the equation of the straight line that passes through the point (3, 4) and perpendicular to the line 3x + 2y + 5 = 0.
Solution:
Q34. If the straight line, 2x - 3y + 17 = 0 is perpendicular to the line passing through the points (7, 17) and (15, β), then β equals
5
-5
JEE Main - 2019A
B
C
D
Solution:
Q35. Find the equation of the straight line which passes through the origin and makes angle 60° with the line
Solution:
Solution:
Q36. A line intersects the straight lines 5x - y - 4 = 0 and 3x - 4y - 4 = 0 atA and B, respectively. If a point P(1, 5) on the line AB is such that AP : PB = 2 : 1 (internally), find point A.
Solution:
Q37. If the foot of the perpendicular from the origin to a straight line is at the point (3, -4). Then find the equation of the line.
Solution:
Q38. Find the equation of a straight line which makes an angle of
with the positive direction of x-axis and cuts an intercept of 6 units in the negative direction of y-axis.
Solution:
Q39. A line passes through the point A(2, 0) which makes an angle of 30° with the positive direction of x-axis and is rotated about A in clockwise direction through an angle of 15°. Find the equation of the straight line in the new position.
Solution:
Q40. The line joining the points A(2, 0) and B(3, 1) is rotated about A in the anti-clockwise direction through an angle of 15°. Find the equation of a line in the new position.
Solution:
Q41. Convert the following equation of a line into normal form. 3x + 4y + 5
Solution:
Q42. Reduce into the (i) slope intercept form and also find its slope and y-intercept.(ii) intercept form and also find the lengths of x and y intercepts.(iii) normal form and also find the values of p and ⍺.
Solution:
Q43. In what ratio does the line joining the points (2, 3) and (4, 1) divide the segment joining the points (1, 2) and (4, 3)?
Solution:
Q44. If the straight line, 2x - 3y + 17 = 0 is perpendicular to the line passing through the points(7, 17) and (15, β), then β equals
5
-5
JEE Main - 2019A
B
C
D
Solution:
Q45. Find the measure of the∠ ABC if the coordinates of A, B and C are A(-2, 1), B(2, 3) and C(-2, -4).
Solution:
Q46. Find the equation of a line through (1, 2) that is perpendicular to the line x - 2y + 1 = 0.
x + 2y - 4 = 0
x - 2y - 4 = 0
2x + y - 4 = 0
2x - y - 4 = 0
A
B
C
D
Solution:
Q47. The equation of straight line cutting off an intercept -2 from y-axis and being equally inclined to the axes are
y = x + 2, y = x - 2
y = x - 2, y = x - 2
y = -x - 2, y = x - 2
None of these
A
B
C
D
Solution:
Solution:
tan-1(7)
Q48. The angle between the line x + y = 3 and the line joining the points (1, 1) and (-3, 4) is
None of these
A
B
C
D
Solution:
Q49. Find the angle between the lines
None of these
A
B
C
D
Solution:
Q50. Find angles between the lines
35°
45°
30°
60°
A
B
C
D
Solution:
Q51. The triangle formed by the lines x + y = 0, 3x + y = 4, x + 3y = 4 is
Isosceles
Right angled
Equilateral
None of these
A
B
C
D
Solution:
Q52. Two lines are drawn trough (3, 4) each of which makes angle of 45° with line x - y = 2, then area of the triangle formed by these lines is
9 sq units
2 sq units
A
B
C
D
Solution:
Q53. The inclination of the straight line passing through the point (-3, 6) and the mid-point of the line joining the points (4, -5) and (-2, 9) is
A
B
C
D
Solution:
Q54. The equations of the lines through (1, 2) which make equal angles with
x = 1, y = 2
x = 2, y = 1
A
B
C
D
Solution:
Q55. Find the equations of the lines through the line makes an angle 45° with the line x - 2y = 3.
Solution:
Q56. A vertex of an equilateral triangle is (2, 3) and the equation of the opposite side x + y = 2. Find the equation of the other sides of the triangle.
Solution:
Solution:
Q57. A line 4x + y = 1 through the point A(2, -7) meets the line BC, whose equation is 3x - 4y + 1 = 0 at the point B. Find the equation of the line AC so that AB = AC.
Solution:
Q58. Find the equations of straight lines passing through (-2, -7) and having an intercept of length 3 between the straight lines 4x + 3y = 12 and 4x + 3y = 3.
Solution:
Q59. Find the equations of the lines passing through the point (2, 3) and equally inclined to the lines 3x - 4y = 7 and 12x - 5y + 6 = 0.
Solution:
Solution:
Q60. In triangle ABC, equation of the right bisectors of the sides AB and AC arex + y = 0 and y - x = 0 respectively. If A = (5, 7) then find the equation of side BC.
Solution:
Q61. The coordinates of the foot of perpendicular from the point (2, 3) on the line y = 3x + 4 is given by
A
B
C
D
Solution:
(1, -1)
Q62. A point equidistant from the lines 4x + 3y + 10 = 0, 5x - 12y + 26 = 0 and 7x + 24y - 50 = 0 is
(0, 0)
(1, 1)
(0, 1)
A
B
C
D
Solution:
Q63. Find the image of the point (4, -13) in the line 5x + y + 6 = 0.
Solution:
Q64. Find the foot of the perpendicular from the point (2, 4) upon x + y = 1.
Solution:
Q65. The distance of the point of intersection of lines 2x - 3y + 5 = 0 and3x + 4y = 0 from the line 5x - 2y = 0 is
A
B
C
D
Solution:
Q66. The length of perpendicular from the point (a cos ⍺, a si ⍺) upon the straight line y = x tan ⍺ + c, c > 0, is
c
c cos ⍺
c sin2 ⍺
c sec2 ⍺
A
B
C
D
Solution:
Q67. Equation of the line passing through (1, 2) and parallel to the line y = 3x - 1 is
y + 2 = x + 1
y - 2 = 3(x - 1)
y + 2 = 3(x + 1)
y - 2 = x - 1
A
B
C
D
Solution:
Q68. The distance of the point (3, 5) from the line 2x + 3y - 14 = 0 measured parallel to line x - 2y = 1, is
A
B
C
D
Solution:
Q69. Find the image of the point (3, 4) with respect to the line y = x.
Solution:
Q70. Area of parallelogram whose sides are 2x + y + 1 = 0, 2x + y + 4 = 0,x - 3y - 1 = 0 and x - 3y + 2 = 0 is equal to______.
A
B
C
D
Solution:
Q71. If t1 and t
2 are roots of the equation t2 + λt + 1 = 0, where λ is an arbitrary
constant. Then, the line joining the points (at1
2, 2 at1) and (at
22 , 2 at
2 ) always
passes through a fixed point whose coordinates are
(a, 0)
(0, a)
(-a, 0)
(0, -a)
A
B
C
D
Solution:
Q72. The point moves such that the area of the triangle formed by it with the points (1, 5) and (3, -7) is 21 sq units. The locus of the point is
6x + y - 32 = 0
x + 6y - 32 = 0
6x - y + 32 = 0
6x - y - 32 = 0
A
B
C
D
Solution:
Q73. The equations of the respective perpendicular bisectors of sides AB and AC of a Δ ABC are x − y + 5 = 0 and x + 2y = 0. If the coordinates of A are (1, –2), then find the equation of BC.
Solution:
Q74. A ray of light is sent along the line x - 2y = 3. Upon reaching the line3x - 2y = 5, the ray is reflected from it. Find the equation of the line containing the reflected ray.
Solution:
Solution:
Q75. A ray of light passing through the point (1, 2) is reflected on the x-axis at a point P and passes through the point (5, 3). Find the abscissa of the point P.
Solution:
Q76. Find equation of straight lines passing through (2, 3) and having an intercept of length 2 units between 2x + y = 3 and 2x + y = 5.
A
BC
(2, 3)
22x + y = 3
2x + y = 5
θ
Solution:
Q77. Equation of diagonals of the square formed by the lines x = 0, y = 0, x = 1 and y = 1 are
y = x, y + x = 1
y = x, y + x = 2
y = 2x, y + 2x = 1
A
B
C
D
Solution:
Q78. Consider the family of lines 5x + 3y - 2 + λ1 (3x - y - 4) = 0 and
x - y + 1 + λ2(2x - y - 2) = 0. Find the equation of a straight line that belongs to
both the families.
Solution:
Q79. Lines 2x + y = 1 and 2x + y = 7 are
on the same side of a point
same lines
on the opposite side of a point
perpendicular lines
A
B
C
D
Solution:
Q80. Find the equation of a line which passes through the intersection point of the lines 3x − 4y + 6 = 0 and x + y + 2 = 0, that is farthest from the point P (2, 3).
Solution:
Q81. The equations of perpendicular bisectors of sides AB and AC of a ΔABC are x - y + 5 = 0 and x + 2y = 0 respectively. If the coordinates of vertex A are (1, -2), then the equation of BC is
23x + 14y - 40 = 0
23x - 14y + 40 = 0
14x - 23y + 40 = 0
14x + 23y - 40 = 0
A
B
C
D
Solution:
Solution:
Q82. The equations of the bisector of the acute angle between the lines3x - 4y + 7 = 0 and 12x + 5y - 2 = 0 is
99x - 27y - 81 = 0
21x + 77y - 101 = 0
11x - 3y + 9 = 0
21x + 77y + 101 = 0
A
B
C
D
Solution:
Q83. The equations of bisectors of the angle between the lines |x| = |y| are
y = ±x and x = 0
y = 0 and x = 0
None of these
A
B
C
D
Solution:
Q84. Find the equation of the bisectors bisecting the angle containing the origin of the straight lines 4x + 3y = 6 and 5x + 12y + 9 = 0.
Solution:
Q85. Find the bisector of the acute angle between the lines x + y = 3 and 7x - y + 5 = 0.
Solution:
Q86. Prove that the length of the perpendicular drawn from any point of the line 7x - 9y + 10 = 0 to the lines 3x + 4y = 5 and 12x + 5y = 7 are the same.
Solution:
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