JEE Main 2021 · MathsMultiple choiceSingle correctMediumApplication

JEE Main 3 August 2021, Shift 1, Maths Q73

Question 73 of 90 in this shift, Maths question 13 of 30, Section A.

If the line

\alpha x + \beta y = 1

touches the hyperbola

\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1

, then the locus of the point

(\alpha, \beta)

(1) $a^2x^2 - b^2y^2 = 1$ Official answer
(2) $b^2x^2 - a^2y^2 = 1$
(3) $a^2x^2 + b^2y^2 = 1$
(4) $b^2x^2 + a^2y^2 = 1$

Official answer

Option 1

NTA final key.

Chapter: Conic Sections
Topic: General Conic Section
Idea tested: Condition for Line to be Tangent

Same idea in other shifts

Asked 7× in all

4 Apr 2025, Shift 2 · Q10Let for two distinct values of p the lines $y=x+p$ touch the ellipse $E:\frac{x^2}{4^2}+\frac{y^2}{3^2}=1$ at the points A and B. Let the…HardSingle correct
25 Jul 2022, Shift 1 · Q28Let the equation of two diameters of a circle $x^2+y^2-2x+2fy+1=0$ be $2px-y=1$ and $2x+py=4p$ . Then the slope $m\in(0,\infty)$ of the…MediumNumerical value
28 Jul 2022, Shift 1 · Q27For the hyperbola $H:x^2-y^2=1$ and the ellipse $E:\frac{x^2}{a^2}+\frac{y^2}{b^2}=1,\ a>b>0$ , let the (1) eccentricity of E be reciprocal…HardNumerical value
24 Jun 2022, Shift 1 · Q15Let $\lambda x-2y=\mu$ be a tangent to the hyperbola $a^2x^2-y^2=b^2$ . Then…MediumSingle correct
24 Jun 2022, Shift 1 · Q28If two tangents drawn from a point $(\alpha, \beta)$ lying on the ellipse $25x^2+4y^2=1$ to the parabola $y^2=4x$ are such that the slope…HardNumerical value
22 Jul 2021, Shift 2 · Q68Let a line $\mathrm{L}:2x+y=k$ , $k>0$ be a tangent to the hyperbola $x^2-y^2=3$ . If $\mathrm{L}$ is also a tangent to the parabola…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.