Let the maximum and minimum values of $\left(\sqrt{8x-x^2-12}-4\right)^2 + (x-7)^2$, $x \in R$ be $M$ and $m$, respectively. Then $M^2-m^2$ is equal to ________.

JEE Main 2024 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 5 April 2024, Shift 2, Maths Q24

Question 24 of 90 in this shift, Maths question 24 of 30, Section B.

Let the maximum and minimum values of

\left(\sqrt{8x-x^2-12}-4\right)^2 + (x-7)^2

x \in R

M

and

m

, respectively. Then

M^2-m^2

is equal to ________.

Official answer

1600

NTA final key.

Chapter: Conic Sections
Topic: Circle Tangents
Idea tested: Maximum and Minimum Distance to a Circle

Same idea in other shifts

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.