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

A set of all points in a plane that are a given

distance, the radius, from a given point, the center

Circle

Standard equation of a circle with center (h,

k) and radius r

(x – h)2 + (y – k)2 = r2

Standard Equation of a Circle

h = -1k= 3r = 2Plug 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

Write the equation of the circle with center (-1,3) and a radius of 2.

a.) center (3,5); radius = 6

b.) center (-2,-1); radius =

c.) center (0, 0); radius = 5

Write the equation of the circle with the given center and radius.

2

You can use this to find the radius of a circle and write the equation.

If r2 = (x-h)2 + (y – k)2, then….

22 )()( kyhxr

h = 2k= 3x= -1y= 1

Write the standard form of the circle with center (2,3) that passes through the point (-1,1).

22 )( kyhxr

22 3121 r

22 23 r

1349 rWrite the equation using h, k, and r:

1332

133222

222

yx

yx

Write the equation for finding radius

Substitute h,k, x and y into equation.

Simplify parenthesis

Find radius by adding numbers under radical

Remember, squaring a square root gets rid of the square root

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.

Find the center and radius of the circle Plot the center Draw radius. Use compass to draw circle with

the given radius.

Graphing a circle:

(x + 7)2 + (y -5)2 = 16

h= -7k= 5r= 4

Center (-7, 5), radius = 4

Find the center and radius of the circle with the given equation. Then graph the circle.

x2 + y2 = 9

Find the center and radius of the circle with the given equation. Then graph the circle.

(x – 2)2 + (y – 3)2 = 100

Find the center and radius of the circle with the given equation. Then graph the circle.

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.

Write the equation of the circles graphed below: