Consider the ellipse

MATHEMATICS · Subjective · CBSE · Mathematics · Conic Sections · Conic Sections

Problem

\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

\Delta ORT

\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}