Question

PLEASE HELP!!! I PUT IN EXTRA POINTS!!!!

Which equation is an equation of a circle with a radius of 4 and its center is at (3, -2)?
Responses

(x - 3)² + (y + 2)² = 16


(x - 3)² + (y + 2)² = 4


(x + 3)² + (y - 2)² = 4


(x + 3)² + (y - 2)² = 16

Answer 1

A. (x - 3)² + (y + 2)² = 16

Explanation:

The formula for a circle plotted on the Cartesian coordinate system is:

`(x - a)^2 + (y - b)^2 = r^2`

where
`(a,b)` is the center of the circle, and
`r` is the length of the circle's radius.

Since the center of the circle in this problem is (3, -2), we know that the left side of the equation should be:

`(x - 3)^2 + (y - (-2))^2`

which can be simplified to:

`(x - 3)^2 + (y + 2)^2`

The radius of the circle is given as 4, so we know that the right side of the equation is:

`4^2`, which is the same as
`16`.

Finally, to answer this question, we can put the two sides of the equation together to get:

`(x - 3)^2 + (y + 2)^2 = 16`