JEE Main 2023 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 11 April 2023, Shift 2, Maths Q27

Question 27 of 90 in this shift, Maths question 27 of 30, Section B.

Let 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 distance of the point

(6, -4)

from the normal to the hyperbola

\alpha^2 x^2 - 9y^2 = 9\alpha^2

at its point

(\alpha - 1, \alpha + 2)

is equal to ________.

Official answer

116

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

26 Jul 2022, Shift 1 · Q13Let the tangent drawn to the parabola $y^2 = 24x$ at the point $(\alpha,\ \beta)$ is perpendicular to the line $2x + 2y = 5$ . Then the…MediumSingle correct
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.