Question

A circle is centered at (-3, 2) and has a radius of 2. What is the equation of the circle?

Answer 1

`color(green)((x+3)^2+(y-2)^2=4)`

Explanation:

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

Substituting `(color(red)(-3),color(blue)(2))` for `color(red)(a),color(blue)(b))`
and `color(purple)(2)` for `color(purple)(r)`
gives
`color(white)("XXX")(x-color(red)(""(-3)))^2+(y-color(blue)(2))^2=color(purple)(2)^2`
or
`color(white)("XXX")color(green)((x+3)^2+(y-2)^2=4)`

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Although this is in "standard circle form" your instructor may prefer "standard polynomial form" which can be obtained by expanding the squared terms and simplifying:
`color(white)("XXX")x^2+y^2+6x-4y+9=0`