ConicsLesson 2: Circles

Mrs. Parziale

Circles

Circle – the set of all points at a given distance from a central point

CENTER = (h, k) RADIUS = rEquation for circles:

r2 = (x – h)2 + (y – k)2

h, k, r are all NUMBERSx, y are VARIABLES

Example 1:

• Given the equation x2 + y2 = 49• What is the center?• What is the radius?• Sketch it.

Example 1:

• Given the equation (x – 4)2 + (y + 3)2 = 9• What is the center?• What is the radius?• Sketch it.

Example 1:

• Given the equation (x + 2)2 + (y – 2)2 < 9• What is the center?• What is the radius?• Sketch it.

Example 4:

Given a circle with center at (0, -1) and a radius of 1. Write a simplified equation for the circle.

r2 = (x – h)2 + (y – k)2

• h = ____• k = ____• r2 = ____

Example 5:

• Write the equation for a circle with a center at (1, 2) and containing the point (3, 4).

r2 = (x – h)2 + (y – k)2

(h, k) = (x, y) =

Example 6:

• Given the equation of a circle,

• What is the center?

• What is the radius?

2 26 3 6 0x x y y

Closure

• For the equation

• Find the radius.• Find the center.• Sketch it.

2 2 4 32 0x y x