Equation of common tangent of $y=x^2$ , $y=-x^2+4x-4$ is/are

y = x², y = -x² + 4x - 4 
Equation of tangent to y = x²  is $\mathrm{y}=\mathrm{mx}-\frac{{\mathrm{m}}^2}{4}$. solving with y = -x² + 4x - 4 4and applying discriminant is 0
We get m = 0, 4 $\Rightarrow$tangent equation are y = 0, y = 4x - 4