The foci of a hyperbola are ( ± 2,0) and its eccentricity is 3/2. A tangent, perpendicular to the line 2 x+3 y=6, is drawn at a point in the first…

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