JEE Main 2021 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 3 August 2021, Shift 2, Maths Q73

Question 73 of 90 in this shift, Maths question 13 of 30, Section A.

A curve passes through the point

(-1, 4)

. If the normal to it at any point

(x, y)

on it passes through

(2, 0)

, then its equation is

(1) $(x-2)^2 + y^2 = 25$ Official answer
(2) $2(x-2)^2 + y^2 = 34$
(3) $2y^2 - (x-2)^2 = 23$
(4) $y^2 - (x-2)^2 = 7$

Official answer

Option 1

NTA final key.

Chapter: Differential Equations
Topic: Tangents and Normals
Idea tested: Finding Curve from Tangent/Normal Properties

Same topic in other shifts

All Tangents and Normals questions

6 Apr 2023, Shift 1 · Q28Let the tangent to the curve $x^2+2x-4y+9=0$ at the point $P(1,3)$ on it meet the $y$ -axis at A. Let the line passing through P and…MediumNumerical value
24 Jun 2022, Shift 1 · Q11If the tangent at the point $(x_1, y_1)$ on the curve $y=x^3+3x^2+5$ passes through the origin, then $(x_1, y_1)$ does NOT lie on the…MediumSingle correct
8 Jan 2020, Shift 1 · Q74Let the normal at a point P on the curve $y^2-3x^2+y+10=0$ intersect the $y$ -axis at $\left(0,\frac{3}{2}\right)$ . If m is the slope of…MediumNumerical value
2 Sep 2020, Shift 1 · Q60If the tangent to the curve $y=x+\sin y$ at a point $(a, b)$ is parallel to the line joining $\left(0, \frac{3}{2}\right)$ and…MediumSingle correct
2 Sep 2020, Shift 1 · Q64Let P(h, k) be a point on the curve $y=x^{2}+7x+2$ , nearest to the line, $y=3x-3$ . Then the equation of the normal to the curve at P is :MediumSingle correct
2 Apr 2017 (offline) · Q72The normal to the curve $y(x-2)(x-3)=x+6$ at the point where the curve intersects the $y$ -axis passes through the point :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 42 of the 174 JEE Main shifts held from 2017 to 2026.