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)} = √(1+9)= √(10)` (units)

Answer:
`√(10)` units