1. CHAPTER 10 CONIC SECTIONS Section 1 - Circles

2. 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.

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

4. 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)

5. Write equations for CIRCLES
Ex. 2) A circle center (4, -2); radius = 8
1) h = 4 k = 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 = *(2√6)2 = 4(6)

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 = √ = √65
r2 = 65
(x + 4)2 + (y + 2)2 = 65

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