Mathematics - Ellipse Question with Solution | TestHub

Consider the ellipse $\frac{x^2}{9}+\frac{y^2}{4}=1$. Let $S(p,q)$ be a point in the first quadrant such that $\frac{p^2}{9}+\frac{q^2}{4}>1$. Two tangents are drawn from $S$ 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 $T$ in the fourth quadrant. Let $R$ be the vertex of the ellipse with positive $x$-coordinate and $O$ be the center of the ellipse. If the area of the triangle $△ORT$ is $\frac{3}{2}$, then which of the following options is correct?