Line tangent to the circle Find the equation of the lines which are tangent to the circle with equation $x^2+y^2=9$ and parallel to the line of equation $x-y+1=0$

Lines parallel to $x-y+1$ have equation $y=x+a$ for $a \in \mathbb{R}$, so common point of circle and $y=x+a$ are solutions of equation:
$$x^2+y^2=x^2+(x+a)^2=9$$
If $y=x+a$ is tangent line, then has only one common point with circle, so equation should has only one solution, so you must have $\Delta=0$.So:
$$x^2+(x+a)^2=x^2+x^2+2ax+a^2=9$$
$$2x^2+2ax+a^2-9=0$$
And $\Delta=(2a)^2-4 \cdot 2(a^2-9)=-4a^2+72=0$
So $a=\pm\sqrt{\frac{72}{4}}$.
