Question

What is the equation of the circle with a center at `(-8 ,3 )` and a radius of `4`?

Answer 1

`(x+8)^2+(y-3)^2=16`

Explanation:

The standard form of a circle with a center at `(h,k)` and a radius `r` is

`(x-h)^2+(y-k)^2=r^2`

Since the center is `(-8,3)` and the radius is `4`, we know that

`{(h=-8),(k=3),(r=4):}`

Thus, the equation of the circle is

`(x-(-8))^2+(y-3)^2=4^2`

This simplifies to be

`(x+8)^2+(y-3)^2=16`