Question

Write an equation for a circle with center at (8,-4) and diameter 12.

Answer 1

We have that the equation of the circle with center at (h,k) and radius r is:

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

in this case, we have that the diameter is 12, then r=6, and we have:

`\begin{gathered} (h,k)=(8,-4) \\ r=6 \\ \Rightarrow(x-8)^2+(y-(-4))^2=(6)^2 \\ (x-8)^2+(y+4)^2=36 \end{gathered}`

therefore, the equation of the circle with center at (8,-4) and diameter 12 is (x-8)^2+(y+4)^2=36