Question

Write an equation in general form of the circle with the given properties. Center at (4,5); r = 2?

Answer 1

$(x-a)^2+(y-b)^2=r^2$

where

$\begin{gathered} (x-4)^2-(y-5)^2=2^2 \\ a=4 \\ b=5 \end{gathered}$$\begin{gathered} x^2-4x-4x+16+y^2-5y-5y+25=4 \\ x^2-8x+y^2_{}-10y+41-4=0 \end{gathered}$

Rearranging yields

$x^2+y^2-8x-10y+37=0$