1. 11.5: Circles in the Coordinate Plane
Objectives: Students will be to…
Identify the center and the radius of a circle from its equation
Write and graph the equation of a circle

2. Circle
A set of all points in a plane that are a given distance, the radius, from a given point, the center

3. Standard Equation of a Circle
Standard equation of a circle with center (h, k) and radius r
(x – h)2 + (y – k)2 = r2

4. Write the equation of the circle with center (-1,3) and a radius of 2.
h = -1 k= 3 r = 2 Plug values into standard equation: (x – (-1))2 +(y – 3)2 = (2)2 (x + 1)2 + (y-3)2 = 4 notice #’s are opposite sign of what is given

5. Write the equation of the circle with the given center and radius.
a.) center (3,5); radius = 6 b.) center (-2,-1); radius = c.) center (0, 0); radius = 5

6. If r2 = (x-h)2 + (y – k)2, then….
You can use this to find the radius of a circle and write the equation.

7. Write the standard form of the circle with center (2,3) that passes through the point (-1,1).
h = 2 k= 3 x= -1 y= 1
Write the equation for finding radius
Substitute h,k, x and y into equation.
Simplify parenthesis
Find radius by adding numbers under radical
Write the equation using h, k, and r:
Remember, squaring a square root gets rid of the square root

8. 1.) center (-2,6); point (-2, 10) 2.) center (7, -2); point (1, -6)
Write the standard form of the circle with the given center that passes through the given point.
1.) center (-2,6); point (-2, 10) 2.) center (7, -2); point (1, -6)

9. Graphing a circle: Find the center and radius of the circle
Plot the center
Draw radius. Use compass to draw circle with the given radius.

10. (x + 7)2 + (y -5)2 = 16 h= -7 k= 5 r= 4 Center (-7, 5), radius = 4
Find the center and radius of the circle with the given equation. Then graph the circle.
(x + 7)2 + (y -5)2 = 16 h= -7 k= 5 r= 4 Center (-7, 5), radius = 4

11. Find the center and radius of the circle with the given equation
Find the center and radius of the circle with the given equation. Then graph the circle.
x2 + y2 = 9

12. Find the center and radius of the circle with the given equation
Find the center and radius of the circle with the given equation. Then graph the circle.
(x – 2)2 + (y – 3)2 = 100

13. A diagram locates a radio tower at (6, -12) on a coordinate grid where each unit represents 1 mile. The radio signal’s range is 80 miles. Find an equation that describes the position and range of the tower.

14. Write the equation of the circles graphed below: