equations of circles. vocab review: circle the set of all points a fixed distance r from a point (h,...
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Finding Equations of Circles You can write an equation of a circle in a coordinate plane if you know its radius and the coordinates of its center.TRANSCRIPT
Equations of Circles
Vocab Review: Circle
The set of all points a fixed distance r from a point (h, k), where r is the radius of the circle and the point (h, k) is the center.
Finding Equations of Circles
• You can write an equation of a circle in a coordinate plane if you know its radius and the coordinates of its center.
6
4
2
-2
5 10 15x
y
(h, k)
(x, y)
Finding Equations of Circles• Suppose the radius is r
and the center is (h, k). Let (x, y) be any point on the circle. The distance between (x, y) and (h, k) is r, so you can use the Distance Formula.
6
4
2
-2
5 10 15x
y
(h, k)
(x, y)
Finding Equations of Circles
• Square both sides to find the standard equation of a circle with radius r and center (h, k).
(x – h)2 + (y – k)2 = r2
If the center is at the origin, then the standard equation is
x2 + y2 = r2.
6
4
2
-2
5 10 15x
y
(h, k)
(x, y)
rkyhx 22 )()(
Equation of a Circle
The center of a circle is given by (h, k)
The radius of a circle is given by r
The equation of a circle in standard form is (x – h)2 + (y – k)2 = r2
The equation of a circle in general form is x2 + y2 + ax + by + c = 0
Writing Equations of Circles
Write the standard equation of the circle:
Center (4, 7) Radius of 5
(x – 4)2 + (y – 7)2 = 25
Writing Equations of Circles
Write the standard equation of the circle:
Center (-3, 8) Radius of 6.2
(x + 3)2 + (y – 8)2 = 38.44
Writing Equations of Circles
Write the standard equation of the circle:
Center (2, -9) Radius of
(x – 2)2 + (y + 9)2 = 11
11
Writing Equations of Circles
Write the standard equation of the circle:
Center (0, 6) Radius of
x 2 + (y – 6)2 = 7
7
Writing Equations of Circles
Write the standard equation of the circle:
Center (-1.9, 8.7) Radius of 3
(x + 1.9)2 + (y – 8.7)2 = 9
Finding the Equation of a Circle Circle A
The center is (16, 10)
The radius is 10
The equation is (x – 16)2 + (y – 10)2 = 100
Finding the Equation of a Circle
Circle B
The center is (4, 20)
The radius is 10
The equation is (x – 4)2 + (y – 20)2 = 100
Finding the Equation of a Circle Circle O
The center is (0, 0)
The radius is 12
The equation is x 2 + y 2 = 144
Graphing Circles
(x – 3)2 + (y – 2)2 = 9
Center (3, 2)
Radius of 3
Graphing Circles
(x + 4)2 + (y – 1)2 = 25
Center (-4, 1)
Radius of 5
Graphing Circles
(x – 5)2 + y2 = 36
Center (5, 0)
Radius of 6
General Form to Standard Form: Completing the Square
