Question

How do you write the equation for a circle with center at (-5, 6) and diameter = 16?

Answer 1

`(x+5)^2+(y-6)^2=64`

Explanation:

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

We are told the center `(a,b)=(-5,6)`
and that the diameter `=16`
which implies the radius is `r=8`

So we have
`color(white)("XXX")(x-(-5))^2+(y-6)^2=8^2`
or
`color(white)("XXX")(x+5)^2+(y-6)^2=64`

Here is the graph for `(x+5)^2+(y-6)^2=64`
graph{(x+5)^2+(y-6)^2=64 [-20.35, 15.68, -3.46, 14.56]}