Question

How do you write the equation for a circle with center (–7 –6) and radius 2?

Answer 1

`(x+7)^2+(y+6)^2=4`

Explanation:

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

Substituting `(color(red)(-7),color(blue)(-6))` for `(color(red)(a),color(blue)(b))`
and color(green)(2)`for`color(green)(r)#

`color(white)("XXX")(x-(color(red)(-7)))^2+(y-(color(blue)(-6)))^2=color(green)(r)^2`

which can be simplified as:
`color(white)("XXX")(x+7)^2+(y+6)^2=4`