10.3 - Circles

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

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 + 2 = ± 9 – (x – 3)2 y = –2 ± 9 – (x – 3)2

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.

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.

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 = 3 k = –1 r 2 = 4, or r = 2 Draw the center (3, –1) and radius 2. Draw a smooth curve.

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

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

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

Find the equation for the circle