Section 1.5: Circles

Definition circle: Set of points a fixed distance from a center point.

Definition radius: Distance from center to any point on the circle.

Section 1.5: Circles1. Sketch the graph of a circle with

center (1,2) and radius = 4

.

. 2. Identify the center and radius

1. Standard Form of the Equation of a Circle

Standard Form:

are the coordinates of the circle center. is the radius of the circle.

(x h)2 (y k)2 r2

),( kh

r

Let be

a point on the circle.

),( yx

2. Write the equation of the circle if you are given the radius and center

3) Write the standard form of the equation of a circle with center at (4, -3) and radius r = 4

4) Determine the x and y intercepts

Find the center and radius from the equation written in standard form

Identify the center and radius for the following equations of circles. Determine the x and y intercepts

5.

6.

7.

434 22 yx

255.31 22 yx

522 yx

Prove (algebraically) that the circle in #6 crosses into the 4th quadrant.

3. Determine the equation of the circle when given 2 points on the circle

8) Determine the equation in standard form for the circle with endpoints of diameter at (4,3) and (0,1).