JEE Main 2021 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 25 July 2021, Shift 2, Maths Q76

Question 76 of 90 in this shift, Maths question 16 of 30, Section A.

If a tangent to the ellipse

x^2+4y^2=4

meets the tangents at the extremities of its major axis at B and C, then the circle with BC as diameter passes through the point :

(1) $(\sqrt3,0)$ Official answer
(2) $(1,1)$
(3) $(-1,1)$
(4) $(\sqrt2,0)$

Official answer

Option 1

NTA final key.

Chapter: Conic Sections
Topic: Ellipse Eccentricity
Idea tested: Coordinates of foci

Same idea in other shifts

Asked 5× in all

7 Apr 2025, Shift 2 · Q13Let $e_1$ and $e_2$ be the eccentricities of the ellipse $\frac{x^2}{b^2}+\frac{y^2}{25}=1$ and the hyperbola…MediumSingle correct
9 Apr 2024, Shift 2 · Q15Let the foci of a hyperbola $H$ coincide with the foci of the ellipse $E:\frac{(x-1)^2}{100}+\frac{(y-1)^2}{75}=1$ and the eccentricity of…MediumSingle correct
25 Jul 2022, Shift 2 · Q14Let the foci of the ellipse $\frac{x^2}{16}+\frac{y^2}{7}=1$ and the hyperbola $\frac{x^2}{144}-\frac{y^2}{\alpha}=\frac{1}{25}$ coincide.…MediumSingle correct
25 Feb 2021, Shift 2 · Q72A hyperbola passes through the foci of the ellipse $\frac{x^2}{25} + \frac{y^2}{16} = 1$ and its transverse and conjugate axes coincide…MediumSingle correct

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.