JEE Main 2020 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 8 January 2020, Shift 2, Maths Q65

Question 65 of 75 in this shift, Maths question 15 of 25, Section A.

If 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 P is :

(1) $3x + 4y = 94$
(2) $x + 3y = 58$
(3) $x + 2y = 42$
(4) $2x + 5y = 100$ Official answer

Official answer

Option 4

NTA final key (Jan 2020).

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

Same idea in other shifts

Asked 6× in all

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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
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.