CHAPTER 10 CONIC SECTIONS Section 1 - Circles

CIRCLES (x – h)2 + (y – k)2 = r2 Center at (h, k) Radius is r = √r2 Notice the formula is minus, so (x – 5)2 would mean h = 5 and (y + 6)2 would mean k = -6 Radius is r = √r2 So if the formula = 36, r2 = 36 and r = 6 for radius.

EXAMPLE 1 (5, 2) (x – 5)2 + (y + 3)2 = 25 1) Identify the center (5, -3) 2) Identify the radius r2 = 25 r = 5 3) Graph the center. (0, -3) (10, -3) (5, -8) 4) Plot edge points DRAW THE CIRCLE.

Practice: (-2, 5) 1) (x+2)2 + (y+1)2 = 36 Center (-2, -1) r = 6 r =3√2 or 4.24 (4, -1) (-8, -1) (-2, -7)

Write equations for CIRCLES Ex. 2) A circle center (4, -2); radius = 8 1) h = 4 k = -2 r = 8 2) (x – 4)2 + (y – -2)2 = 82 3) (x – 4)2 + (y + 2)2 = 64 Practice 1) (x + 3)2 + (y – 5)2 = 81 2) x2 + (y + 7)2 = 24 *(2√6)2 = 4(6)

Write equations for CIRCLES 3) (x + 4)2 + (y + 2)2 = Radius - The distance from the center of a circle to a point on the edge of the circle. ________________ Distance = √(x2 – x1)2 + (y2 – y1)2 r = √(8)2 + (1)2 = √64 + 1 = √65 r2 = 65 (x + 4)2 + (y + 2)2 = 65

Write equations for CIRCLES 4) (x – 4)2 + (y – 1)2 = A = π r2 36π = π r2 *Sub 36π in for area 36 = r2 * Cancel π (x – 4)2 + (y – 1)2 = 36