1. Circles

2. CIRCLE TERMS EQUATION FORM CENTER Radius
Definition: A circle is an infinite number of points a set distance away from a center
EQUATION FORM
CENTER
Radius r
(x – h)² + (y – k)² = r²
(h, k )
C=(h , k) r

3. Circles
Write an equation of a circle with center (3, –2) and radius 3.
(x – h)2 + (y – k)2 = r2 Use the standard form of the equation of a circle.
(x – 3)2 + (y – (–2))2 = 32 Substitute 3 for h, –2 for k, and
3 for r.
(x – 3)2 + (y + 2)2 = 9 Simplify.
Check: Solve the equation for y and enter both functions into your graphing calculator.
(x – 3)2 + (y + 2)2 = 9
(y + 2)2 = 9 – (x – 3)2
y = ± – (x – 3)2
y = –2 ± – (x – 3)2

4. Circles
Write an equation for the translation of x2 + y2 = 16 two units right and one unit down.
(x – h)2 + (y – k)2 = r 2 Use the standard form of the equation of a circle.
(x – 2)2 + (y – (–1))2 = 16 Substitute 2 for h, –1 for k, and 16 for r 2.
(x – 2)2 + (y + 1)2 = 16 Simplify.
The equation is (x – 2)2 + (y + 1)2 = 16.

5. Circles
Write an equation for the translation of x2 + y2 = 25 two units left and three units up.
(x – h)2 + (y – k)2 = r 2
(x – (-2))2 + (y – 3)2 = 25
(x + 2)2 + (y – 3)2 = 25
The equation is (x + 2)2 + (y – 3)2 = 25.

6. Let’s Try One Graph (x – 3)2 + (y + 1)2 = 4.
(x – h)2 + (y – k)2 = r 2 Find the center and radius of the circle.
(x – 3)2 + (y – (–1))2 = 4
h = k = – r 2 = 4, or r = 2
Draw the center (3, –1) and radius 2.
Draw a smooth curve.

7. Let’s Try One
Graph (x + 2)2 + (y + 1)2 = 9.

8. Circles For the equation find the center and the radius.
(x – 3)2 + (y + 2)2 = 9
(x – h)2 + (y – k)2 = r2

9. Circles For the equation find the center and the radius.
(x – 4)2 + (y + 1)2 = 13
(x – h)2 + (y – k)2 = r2

10. Find the equation for the circle