JEE 2023 — Mathematics PYQ

The foci of a hyperbola are $(\pm 2,0)$ and its eccentricity is $\frac{3}{2}$. A tangent, perpendicular to the line $2x+3y=6$, is drawn at a point in the first quadrant on the hyperbola. If the intercepts made by the tangent on the $x$ and $y$-axis are $a$ and $b$, respectively, then $|6a|+|5b|$ is equal to ______.