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Lesson Plan #68

Class: Geometry Date: Monday March 9th, 2020

Topic: Equation of a circle. Aim: How can we graph a circle given its equation?

Objectives:

1) Students will be able graph a circle given its equation

2) Students will be able to write the equation of a circle given information about the circle

HW #68: Pages 7 and 8

Do Now:

1) Graph point O at the origin.

2) Sketch the graph of all points that are 5 units away from the origin

(Try using a compass)

3) What kind of figure have you graphed?

PROCEDURE:

Write the Aim and Do Now

Get students working! Take attendance Give Back HW

Collect HW

Go over the Do Now

Assignment #1:

Given a circle with center (ℎ, 𝑘) and a point on the circle (𝑥, 𝑦), find the length of the radius.

Equation of a circle with center (𝒉, 𝒌) and radius 𝒓is given by:

(𝑥 − ℎ)2 + (𝑦 − 𝑘)2 = 𝑟2

Example #1:

Find the center and radius of the circle with the equation. Sketch the graph of the circle (𝑥 + 3)2 + (𝑦 − 5)2 = 4

Exercise 1:

Find the center and radius of each circle. Sketch the graph.

A) (𝑥 − 2)2 + (𝑦 + 4)2 = 9 B) (𝑥 + 7)2 + (𝑦 + 3)2 = 25 C) 𝑥2 + (𝑦 − 1)2 = 49

2 Exercise #2:

Write an equation of a circle with the given center and radius

A) C(0,0); r = 9 B) C(-3,-8); r = 6 C) C(1,-2); r = √3

Exercise #3:

Exercise #4:

Exercise #5:

Exercise #6:

D. What is the area of the circle? _____________

E. Is the point represented by coordinates (-7, 12) in the circle, on the circle or outside the circle? _______

Explain _______________________________________________________________________________

3 Group Work: Within your groups discuss the solutions to the problems below. Justify your explanations to your group

members.

1) Write a transformation of a circle that would result in the circumference of the circle being different from the circumference of

its image?

2) A) Write the equation of each circle at the right.

B) Find the circumference of each circle below

C) Find the ratio of the area of smaller circle to the area of the bigger circle

D) The area of the bigger circle is how many times greater than the area of the smaller circle?

E) Write a transformation or sequence of transformations that would map the smaller circle onto the bigger.

2) The endpoints of a diameter of a circle are (-1,-4) and (5,4).

A) Find the coordinates of the center of the circle.____________

B) Find the length of the radius of the circle. ____________

C) Find an equation of the circle. _________________

D) Find the circumference and area of the circle. _______________

E) Use a compass to construct the circle. _________________

F) Via construction, inscribe an equilateral triangle in the circle.

G) Graph the image of the circle after reflecting through the line

1y .

H)Write the equation of the image of the original circle after the line

reflection in G. ________________________

4 3) If circle A is the image of circle B, under which transformation will the circles not be congruent?

(1) Reflection over the x-axis

(2) Translation to the left 5 and down 4

(3) Dilation centered at the origin with scale factor 2

(4) Rotation of 270° counterclockwise about the origin 3

4) In the diagram at the right a circle is graphed on the coordinate plane. Which

transformation does not carry the circle onto itself?

A) A reflection over 2y B) A reflection over 4x

C) (4, 2),90oR

D) 2,5T

5A)

5B) The constant of dilation that maps circle C onto circle C’ is 1.5. If the area of circle C is 36 square units, find

the area of the circle C’.

6)

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H.O.T. Questions:

1) Write the equations of the circle if the points with coordinates 8,3 , 4,7 , and 4, 1 .

Draw in the circle

Find the area of the circle

Draw the image of the circle after a dilation, centered at the origin with a scale factor of ½.

2) Find the point(s) of intersection, if any, between the circle with equation 2 21 4x y and the line with

equation 1y x

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3) Write the equation of the circle centered at (1,1) and passing through the point with coordinates 7,7

Graph the circle

Inscribe an equilateral triangle in the circle

4) A circle with a diameter of 12 has its center in the 2nd quadrant. The lines 4y and 1x are tangent to the circle.

Write the equation of the circle

Graph the circle

Write the equation of the image of the circle after a dilation, with a scale factor of 3, centered at the origin

What is the ratio of the area of the image to the area of the pre-image

7 HW#68: Name _________________________________________ Date _________________ Per. _________

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