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Ellipse question

2024 · Shift 1 · Q21

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PYQ Library
JEE Advanced
Mathematics
Ellipse
2024 · Shift 1 · Q21

Ellipse question

2024 · Shift 1 · Q21

JEE AdvancedMathematicsEllipseMCQ+3 / −1

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}\gt 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
$q=1, p=6 \sqrt{3}$

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