Question

How do you find the equation of a circle center of (5,-2) and a radius of 2?

Answer 1

`(x-5)^2+(y+2)^2=4`

Explanation:

I'm sure there a better answer and explanation but from my little experience with geometry I know the following:
1. `x^2+y^2=r^2` is the equation of a circle center of (0,0) and a radius of r.
2. to move the center you just need to move the points of x and y.

so a movement of 5 points in the positive direction of the x axis is translated to
`(x-5)^2` instead of `(x^2)`
a movement of 2 in the negative direction of the y axis is translated to
`(y+2)^2` instead of `(y^2)`

which then lead to the equation
`(x-5)^2+(y+2)^2=2^2`

Answer 2

`(x-5)^2+(y+2)^2=4`

Explanation:

The generic equation of a circle with center `(h,k)` and radius `r` is `(x-h)^2+(y-k)^2=r^2`.

With a center of `(5,-2)` and a radius of `2`, you have
`(x-5)^2+(y-(-2)^2)=2^2`
or
`(x-5)^2+(y+2)^2=4`.