Consider a ellipse $\frac{x^2}{9}+\frac{y^2}{4}=1$ Let $R(b,c)$ be a point in the first quadrant such that $\frac{b^2}{9}+\frac{c^2}{4}>1$. Two tangents are drawn from $R$ to the ellipse, of which one meets the ellipse at one end point of the minor axis and the other meets the ellipse at a point $Q$ in the forth quadrant. Let $P$ be the vertex of the ellipse with positive $x$-coordinate and $O$ be the center of the ellipse. If the area of the triangle $\triangle OPQ$ is $\frac{3}{2}$, If the value of $b$ is "$g\sqrt{g}$" and the value of $c$ is "$h$". Then find out $g+h$.

Geometry Equation

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