The slope of the tangent at the point $(h,h)$ of the circle $x^2+y^2=a^2$, is 

The equation of the tangent at $(h,h)$ to the circle $x^2+y^2=a^2$ is $hx+hy=a^2$

$\therefore$ Slope of the tangent $=\frac{-h}{h}=-1$