Let the eccentricity of the hyperbola H: x^2/a^2-y^2/b^2=1 be √(5/2) and length of its latus rectum be 6 √ 2, If y=2 x+c is a tangent to the…

Let the eccentricity of the hyperbola $\displaystyle H: \frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ be $\displaystyle \sqrt{\frac{5}{2}}$ and length of its latus rectum be $\displaystyle 6 \sqrt{2}$, If $\displaystyle y=2 x+c$ is a tangent to the hyperbola $\displaystyle H$, then the value of $\displaystyle c^2$ is equal to