warm-up . what do we need to keep the same? what do we need to change?

Warm-up

What do we need to keep the same?

What do we need to change?

Chapter 8Conic Sections

“Circles”

What do you need to graph a circle? Center (h, k) Radius = r Standard form of a circle:

(x - h)2 + (y - k)2 = r2

Examples Ex: x2 + y2 = 25

Center (0, 0) Radius = 5

Ex: (x-2)2 + (y+4)2 = 49 Center (2, -4) Radius = 7

State the center and the radius for each: (x + 4)2 + (y - 6)2 = 36

(x + 1)2 + (y - 3)2 = 49

(x + 3)2 + (y + 90)2 = 50

(x + 37)2 + (y - 12)2 = 50

State the center and the radius x2 + 2x + 1 + y2 = 4

x2 + y2 – 4y – 16 = 0

x2 – 4x + 5 + y2 + 2y = 25

Graphing Circles x2 + y2 = 25

(x-2)2 + (y+4)2 = 49

Now you graph these on your own! (x - 3)2 + (y - 1)2 = 9 (x - 5)2 + (y - 4)2 = 16

Graph on your own… (x - 1)2 + (y - 5)2 = 25 (x + 2)2 + (y - 7)2 = 36

Keep going! (x + 7)2 + (y + 5)2 = 49 (x + 8)2 + (y + 10)2 = 50

Write the equation of the circle Center (-4, 3) radius = 4

Center (5, -2) radius = 8

Center (-2, 3) radius = 3

Write the equation of the circle For the translation of x2 + y2 = 9 four units left and three units up.

For the translation of x2 + y2 = 1 five units left and three units down.

For the translation of x2 + y2 = 4 two units right and seven units up.

Homework! Worksheet