Circle equation and tangent line

Question

Give the equation of the line that passes through the center of the circle described by $x^2−8x+y^2+6y=50$ and is perpendicular to the line given by $x+2y=5$.

Answer 1

The center of the circle is given by: $(4,-3)$

Now any line $\perp$ to $x+2y=5$ is given by: $2x-y+k=0$ and this line passes through $(4,-3)$.

So, $2\times4-(-3)+k=0\implies k=-11$.

So the equation is given by: $2x-y-11=0$ or, $2x-y=11$.