JEE Advanced 2023 Paper 2 · Mathematics · Conic Sections · medium

(x^2/(9)+(y^2/(4)=1.

One or more options correct

Consider the ellipse

E:\ \dfrac{x^2}{9}+\dfrac{y^2}{4}=1

. Which of the following statements is/are correct?

A. The minimum area of the triangle formed by a tangent to $E$ with the coordinate axes (in the first quadrant) is $6$
B. The locus of the point from which perpendicular tangents are drawn to $E$ is $x^2+y^2=11$
C. The product of the perpendicular distances of the two foci from any tangent to $E$ is $9$
D. The length of a latus rectum of $E$ is $\dfrac43$

Show answer and solution

Answer: A

(A) The tangent at

(3\cos\theta,2\sin\theta)

has intercepts

\frac3{\cos\theta},\frac2{\sin\theta}

, so the triangle area is

\frac{3}{\sin\theta\cos\theta}=\frac{6}{\sin2\theta}\ge6

: true. (B) The director circle is

x^2+y^2=a^2+b^2=13

, not

11

: false. (C) The product of the focal perpendicular distances to any tangent equals

b^2=4

, not

9

: false. (D) The latus rectum is

\frac{2b^2}{a}=\frac83

, not

\frac43

: false. Only (A) is correct.

Original question written in the JEE Advanced 2023 Paper 2 pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake