JEE Main 2022 · MathsNumerical answerNumerical valueMediumMulti-step

JEE Main 25 July 2022, Shift 1, Maths Q28

Question 28 of 90 in this shift, Maths question 28 of 30, Section B.

Let the equation of two diameters of a circle

x^2+y^2-2x+2fy+1=0

2px-y=1

and

2x+py=4p

. Then the slope

m\in(0,\infty)

of the tangent to the hyperbola

3x^2-y^2=3

passing through the centre of the circle is equal to ______.

Official answer

NTA final key (2022 Session 2).

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
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
3 Aug 2021, Shift 1 · Q73If 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…MediumSingle correct
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.