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 $\triangle O R T$ is $\frac { 3 } { 2 }$, then which of the following options is correct? (A) $q = 2 , p = 3 \sqrt { 3 }$ (B) $q = 2 , p = 4 \sqrt { 3 }$ (C) $q = 1 , p = 5 \sqrt { 3 }$ (D) $q = 1 , p = 6 \sqrt { 3 }$
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 $\triangle O R T$ is $\frac { 3 } { 2 }$, then which of the following options is correct?
(A) $q = 2 , p = 3 \sqrt { 3 }$
(B) $q = 2 , p = 4 \sqrt { 3 }$
(C) $q = 1 , p = 5 \sqrt { 3 }$
(D) $q = 1 , p = 6 \sqrt { 3 }$