Chapter 1.4, Problem 68AYU

Challenge Problem. If $x^2+y^2+dx+ey+f=0$ is the equation of a circle, show that

$x_{0}x+y_{0}y+d\left(\frac{x+x_0}{2}\right)+e\left(\frac{y+y_0}{2}\right)+f=0$

is an equation of the tangent line to the circle at the point $(x_0,y_0).$