Question

the equation of a circle centered at (-4,2) through the point (5,10)

Answer 1

example:
Find an equation for the circle centered at (–5, 12)
and passing through the point (–2, 8).


The Distance Formula will give me the radius, which is, after all, the distance between the center and any point on the circle.

d = sqrt[(-5 - (-2))^2 + (12 - 8)^2] = sqrt[(-3)^2 + (4)^2] = sqrt[9 + 16] = sqrt[25] = 5 = r

Then the center-radius form of the equation is:

(x – (–5))2 + (y – (12))2 = 52
(x + 5)2 + (y – 12)2 = 25