Question

Write the equation of the circle with a center at ( 2, -4 ) and a radius of 4

Answer 1

`\textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{2}{ h},\stackrel{-4}{ k})\qquad \qquad radius=\stackrel{4}{ r} \\\\\\\ [x-2]^2~~ + ~~[y-(-4)]^2~~ = ~~4^2\implies (x-2)^2~~ + ~~(y+4)^2~~ = ~~16`