Let the quadratic curve passing through the point $(-1, 0)$ and touching the line $y = x$ at $(1, 1)$ be $y = f(x)$. Then the $x$-intercept of the normal to the curve at the point $(\alpha, \alpha + 1)$ in the first quadrant is _________.

JEE Main 2023 · MathsNumerical answerNumerical valueMediumMulti-step

JEE Main 10 April 2023, Shift 2, Maths Q25

Question 25 of 90 in this shift, Maths question 25 of 30, Section B.

Let the quadratic curve passing through the point

(-1, 0)

and touching the line

y = x

(1, 1)

y = f(x)

. Then the

x

-intercept of the normal to the curve at the point

(\alpha, \alpha + 1)

in the first quadrant is _________.

Official answer

NTA final key.

Chapter: Application of Derivatives
Topic: Tangents and Normals
Idea tested: Intercepts of Tangent and Normal

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Asked 3× in all

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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.