Let $L$ be a tangent line to the parabola $y^2=4x-20\text{ at }(6,2)$. If $L$ is also a tangent to the ellipse $\frac{x^2}{2}+\frac{y^2}{b}=1$, then the value of  $b$ is equal to 

Equation of tangent to the parabola $y^2=4x-20\text{ at }(6,2)\text{ is }2y=2(x+6)-20\Rightarrow y=x+6-10$

$\Rightarrow x-y-4=0\Rightarrow y=x-4$

$y=x-4\text{ is a tangent to the ellipse }\frac{x^2}{2}+\frac{y^2}{b}=1\Rightarrow (-4{)}^2=2(1{)}^2+b\Rightarrow b=14\text{. }$