Question

A circle has a center of (5,-5) and goes through (6,-2). What is the radius?

Answer 1

Let O(5, -5) be the center of the circle, and P(6, -2) be a point on this circle.

The distance between points O and P, that is |OP|, is the radius of this circle, 

We use the distance between 2 points formula:

|OP|=$\sqrt{ (x_2-x_1)^{2} + (y_2-y_1)^{2} }= \sqrt{ (6-5)^{2} + (-2-(-5))^{2} }$
$= \sqrt{ 1^{2}+ (-2+5)^{2}} = \sqrt{1+9}= \sqrt{10}$ (units)

Answer: $\sqrt{10}$ units