Coordinate Geometry: JEE Main 2022 Mathematics question

Let the eccentricity of the hyperbola $H:{{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1$ be $\sqrt {{5 \over 2}}$ and length of its latus rectum be $6\sqrt 2$. If $y = 2x + c$ is a tangent to the hyperbola H, then the value of c² is equal to :