Question

Find the standard form of the equation of the circle that passes through (2,-2) and concentric with the circle centered at (2,1) and radius 1?

Answer 1

`(x - 2)^2 + (y-1)^2 = 9`

Explanation:

The standard form for the equation for a circle with center `(a,b)` and radius `r` is

`(x-a)^2 + (y-b)^2 = r^2`

Since our circle is concentric (shares a center) with a circle centered at `((2,1)`, that's the center of our circle `(a,b)=(2,1)`. The radius of the other circle is irrelevant.

We know `(2,2)` is on circle. We want the equation for a circle centered at `(2,1)` which has `(2,-2)` on it.

Since the distance from `(2,1)` to `(2,-2)` is `3,` the equation is

`(x - 2)^2 + (y-1)^2 = 3^2`

Here's a graph:

graph{(x - 2)^2 + (y-1)^2 = 3^2 [-7.125, 12.875, -3.36, 6.64]}