Question

How do you find the equation of the circle with center `(–7, –6)` and radius `2`?

Answer 1

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

Explanation:

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

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

From the information provided, we know that `h=-7,k=-6,` and `r=2`, hence the equation

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

Which yields, when simplified

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

Graphed:

graph{((x+7)^2+(y+6)^2-4)((x+7)^2+(y+6)^2-.02)=0 [-17, 5, -10, 1]}