Standard Equation of a Circle

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’s 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’s endpoints. (4, 0)
The radius is 1/2 the length of the diameter…
Using the distance formula to find the length:



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