Question

Write the equation in standard form for the circle with center (5,0) passing through (-1, 9/2)

Answer 1

(x - 5)^2 + y^2 = 225/4,

or you could write it as (x - 5)^2 + y^2 = 56.25.

Explanation:

The factor form is

(x - h)^2 + (y - k)^2 = r^2 where the center is (h, k) and r = the radius.

So we have:

(x - 5)^2 + (y - 0)^2 = r^2

As the point (-1, 9/2) is on the line:

(-1 - 5)^2 + (9/2)^2 = r^2

r^2 = 36 + 81/4

r^2 = 225/4.

So substituting for r^2:

(x - 5)^2 + (y - 0)^2 = 225/4

(x - 5)^2 + y^2 = 225/4 is the standard form.