JEE Main 2023 · MathsNumerical answerNumerical valueMediumMulti-step

JEE Main 6 April 2023, Shift 1, Maths Q28

Question 28 of 90 in this shift, Maths question 28 of 30, Section B.

Let 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 parallel to the line

x-3y=6

meet the parabola

y^2=4x

at B. If B lies on the line

2x-3y=8

, then

(AB)^2

is equal to ____________

Official answer

292

NTA final key.

Chapter: Conic Sections
Topic: Tangents and Normals
Idea tested: Equation of Tangent

Same topic in other shifts

All Tangents and Normals questions

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
3 Aug 2021, Shift 2 · Q73A 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 isMediumSingle 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.