JEE Main Maths · Conic Sections

Condition for Line to be Tangent

Condition for Line to be Tangent (Conic Sections) was asked 5 times in 4 JEE Main shifts, 2022–2025, out of the 42 shifts Lumi analysed. 3 of the 5 had a numerical answer.

Times asked: 5; in 4 shifts
Years: 2022–2025
Usual format: Numerical value; Multi-step
Pattern: Occasional; repeats across shifts

How it is asked

Area of quadrilateral from ellipse tangents
Condition for line tangent to hyperbola

Difficulty

Easy 0Medium 2Hard 3

Where it sits

Chapter: Conic Sections. Topic: General Conic Section, 14 questions over 6 ideas.

All 5 questions

Newest first, each with its options and official answer.

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