2. Aim: What is the standard equation of a circle? Do Now: The endpoints of a diameter of a circle are P(6,1) and Q(-4,-5). Find the coordinates of the center and the length of the radius. Center: (1,-2) HW: Worksheet

3. What is the equation of a circle? There are two types of forms of a circle. (x – h) 2 + (y – k) 2 = r 2 Center-radius form (x – h) 2 + (y – k) 2 = r 2 The equation for the circle from Do Now is Standard form x 2 + y2 + Dx + Ey + F = 0

4. Find the center and radius of the circle whose equation is In order to find the center and radius, we first need to write the equation in center-radius form Complete the squares for x 2 – 4x and y 2 + 6y (x 2 – 4x + 4)+(y 2 + 6y + 9) = 3 + 13 Center: (2,-3) radius = 4

5. The standard form of a circle is x 2 + y 2 + 3x – 4y – 14 = 0. Find the center and radius Center: Radius =

6. The center of the circle is C(-1,1) and point P(-1,5) is on the circle. Write the equation in a) center-radius form b) standard form a) (x + 1) 2 + (y – 1) 2 = 16 b) x 2 + 2x +1 + y 2 – 2y + 1 – 16 = 0 x 2 + y 2 + 2x – 2y – 14 = 0

7. Find the center and radius for #1 and #2 1. 2. 3. Write a) center-radius form b) standard form Center C(1,1) a point P(6,13) on the circle (1,1) r = 3 (3,-1) r = 4 a) (x – 1) 2 + (y – 1) 2 = 169 b) x 2 + y 2 – 2x – 2y – 167 = 0