Question

15. center at (-2, 0), diameter 16
equation

Answer 1

`(x+2)^(2)+y^(2)=64`

Explanation:

The equation of a circle is given by
`(x-h)^(2)+(y-k)^(2)=r^(2)`, where
`(h,k)` is the center and
`r` is the radius.

Substitute the points for
`h` and
`k` and simplify.

`(x-(-2))^(2)+(y-0)^(2)=r^2`

`(x+2)^2 + y^2 =r^2`

The diameter is given and the radius is half the length of the diameter, so the radius is 8

Substitute for
`r`

`(x+2)^2 +y^2 =8^2`

`(x+2)^2 +y^2 =64`