Question

What is the standard form of the equation of a circle with a center (7, 3) and a diameter of 24?

Answer 1

`(x - 7)^2 + (y-3)^2 = 144`

Explanation:

The standard form of a circle centered at `(x_1, y_1)` with radius `r` is
`(x-x_1)^2 + (y-y_1)^2 = r^2`

The diameter of a circle is twice its radius. Therefore a circle with diameter `24` will have radius `12`. As `12^2 = 144`, centering the circle at `(7, 3)` gives us

`(x - 7)^2 + (y-3)^2 = 144`