Question

How do you write an equation of a circle whose center (-1, 2) and radius 4?

Answer 1

`(x+1)^2+(y-2)^2=16`

Explanation:

The general 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`

Given `(color(red)(a),color(blue)(b))=(color(red)(-1),color(blue)(2))`
and `color(green)(r)=color(green)(4)`
this becomes
`color(white)("XXX")(x-(color(red)(-1)))^2+(y-color(blue)(2))^2=4^2`

which would normally be simplified as
`color(white)("XXX")(x+1)^2+(y-2)^2=16`