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Ellipse question

2025 · Shift 2 · Q23

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PYQ Library
JEE Advanced
Mathematics
Ellipse
2025 · Shift 2 · Q23

Ellipse question

2025 · Shift 2 · Q23

JEE AdvancedMathematicsEllipseMultiple correct+4 / −2

Let

P\left(x_1, y_1\right)

and

Q\left(x_2, y_2\right)

be two distinct points on the ellipse

\frac{x^2}{9}+\frac{y^2}{4}=1

such that

y_1\gt 0

, and

y_2\gt 0

. Let

C

denote the circle

x^2+y^2=9

, and

M

be the point

(3,0)

. Suppose the line

x=x_1

intersects

C

at

R

, and the line

x=x_2

intersects C at

S

, such that the

y

-coordinates of

R

and

S

are positive. Let

\angle R O M=\frac{\pi}{6}

and

\angle S O M=\frac{\pi}{3}

, where

O

denotes the origin

(0,0)

. Let

|X Y|

denote the length of the line segment

X Y

. Then which of the following statements is (are) TRUE?

A
The equation of the line joining P and Q is $2x + 3y = 3(1 + \sqrt{3})$
B
The equation of the line joining P and Q is $2x + y = 3(1 + \sqrt{3})$
C
If $N_2 = (x_2, 0)$ , then $3|N_2Q| = 2|N_2S|$
D
If $N_1 = (x_1, 0)$ , then $9|N_1P| = 4|N_1R|$

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