May 20, 2013
11.7 Equations of Circles
(x,y)
r
C(h,k)
The equation of a circle with Center (h,k) and
radius, r, is
2
(x-h)2 + (y-k) = r 2
May 20, 2013
State the center and radius of the following circles.
2
2
1. (x - 3) + (y + 4) = 25
2. x2 + (y - 3)2 = 9
2
3. x + y 2 = 49
May 20, 2013
Write the equation of the circle with the following.
4. C(-5,0) and r = 4
5. C(5,2) and r = 1
May 20, 2013
6. C(4,-3) and passes through (2,1)
May 20, 2013
7. Sketch the circle: (x-2) 2 + (y+3) 2 = 9
May 20, 2013
To determine where a point is with respect to a circle,
substitute the point for x and y and evaluate. If:
2
2
2
2
2
(x - h) + (y - k) < r then pt. is inside of circle
(x - h) + (y - k) > r 2 then pt. is outside of circle
2
2
(x - h) + (y - k) = r 2 then pt. is on the circle
May 20, 2013
8. Where is each point with respect to the circle?
2
2
(x - 13) + (y - 6) = 9
a. (5,6)
b. (14,8)
c. (20,9)
May 20, 2013
9. An amateur radio operator wants to build a radio
antenna near his home without using his house as a bracing
point. He uses 3 poles to brace the antenna. The poles are
to be inserted in the ground at three points equidistant
from the antenna located at A(4,4), B(-3,-1), and L(2,-8).
What are the coordinates of the base of the antenna?