# Circle equation

Note:  If r2 is not a perfect square then leave r in simplified radical form but use the decimal equivalent for graphing.  Example:

1) Graph the following circle:

1. (x - 3)2 + (y + 1)2 = 4
2.  (x – 2)2 + (y – 5)2 = 9
3.  (y + 4)2 + (x + 2)2 = 16

2) For each circle: Identify its center and radius.

a. (x + 3)2 + (y – 1)2 = 4

Center:_____________

b. x2 + (y – 3)2 = 18

Center:___________

c. (y + 8)2 + (x + 2)2 = 72

Center:_____________

3) Write the equation of the following circles:

4) Give the equation of the circle that is tangent to the y-axis and center is (-3, 2).

Putting Equations in Standard Form

Example 1:  x2 + y2 + 6x – 8y – 11 = 0                                   Example 2: x2 + y2 – 2x +  6y – 10 = 0

(x2 + 6x) + (y2 – 8y) = 11

(x2 + 6x + 9) + (y2 – 8y + 16) = 11 + 9 + 16

(x + 3)2  + (y – 4)2 = 36

6) Find the standard form, center, and radius of the following circles:

6a) x2 + y2 – 4x + 8y – 5 = 0

Center:___________

6b) 4x2 + 4y2 + 36y + 5 = 0

Center:________

7) Graph the following circles:

7a) x2 – 2x + y2 + 8y – 8 = 0

7b) x2 + y2 – 6x + 4y – 3 = 0

8) Give the equation of the circle whose center is (5,-3) and goes through (2,5)

9) Give the equation whose endpoints of a diameter at (-4,1) and (4, -5)

10) Give the equation of the circle whose center is (4,-3) and goes through (1,5)

11) Give the equation whose endpoints of a diameter at (-3,2) and (1, -5)

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