Mathematics Question from JEE Main 2023 · 13 April, Shift 2

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