Question

Given the equation of a circle: `(x-3)^2+(y+2)^2=25`, how do you find the center and the radius?

Answer 1

center: `(3,-2)`
radius: `5`

Explanation:

The general form for the equation of a circle with center `(color(red)(a),color(blue)(b))` and radius `color(green)(r)` is
`color(white)("XXX")(x-color(red)(a))^2+(y-color(blue)(b))^2=color(green)(r)^2`

`(x-3)^2+(y+2)^2=25`
can be easily transformed into the general form as:
`color(white)("XXX")(x-color(red)(3))^2+(y-color(blue)((-2)))^2=color(green)(5)^2`