JEE Main 2022 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 26 July 2022, Shift 1, Maths Q13

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

Let the tangent drawn to the parabola

y^2 = 24x

at the point

(\alpha,\ \beta)

is perpendicular to the line

2x + 2y = 5

. Then the normal to the hyperbola

\frac{x^2}{\alpha^2} - \frac{y^2}{\beta^2} = 1

at the point

(\alpha + 4,\ \beta + 4)

does NOT pass through the point :

(1) $(25,\ 10)$
(2) $(20,\ 12)$
(3) $(30,\ 8)$
(4) $(15,\ 13)$ Official answer

Official answer

Option 4

NTA final key.

Chapter: Conic Sections
Topic: Normals to Conics
Idea tested: Hyperbola Normal Point Form

Same idea in other shifts

Asked 6× in all

11 Apr 2023, Shift 2 · Q27Let the tangent to the parabola $y^2 = 12x$ at the point $(3, \alpha)$ be perpendicular to the line $2x + 2y = 3$ . Then the square of…HardNumerical value
25 Jun 2022, Shift 2 · Q29Let the eccentricity of the hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$ be $\frac{5}{4}$ . If the equation of the normal at the point…HardNumerical value
26 Jun 2022, Shift 2 · Q13The normal to the hyperbola $\frac{x^2}{a^2} - \frac{y^2}{9} = 1$ at the point $(8, 3\sqrt{3})$ on it passes through the point :MediumSingle correct
8 Jan 2020, Shift 2 · Q65If a hyperbola passes through the point $\mathrm{P}(10, 16)$ and it has vertices at $(\pm 6, 0)$ , then the equation of the normal to it at…MediumSingle correct
4 Sep 2020, Shift 1 · Q66Let P(3, 3) be a point on the hyperbola, $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$ . If the normal to it at P intersects the $x$ -axis at (9,…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.