Standard Equation of a Circle

(x – h)² + (y – k)² = r²

(h, k) is the center r is the radius

Example: What is the equation of a circle with diameter 20 and its center translated 8 units to the left and 11 units up from the origin?

since diameter is 20, radius is 10…
origin shifted 8 units to the left: (-8
origin shifted 11 units up: (-8, 11)

(x-h)² + (y-k)² = r²
(x + 8)² +(y- 11)² = 100

Example: A circle is diameter has endpoints (1, 4) and (7, -4).

What is the equation of the circle?

To determine the equation of a circle, we need the center and the radius.
Center is the midpoint of the diameter is endpoints. (4, 0)
The radius is 1/2 the length of the diameter…
Using the distance formula to find the length: