Verified Solution • 2025–26 Session moderate

QJEEM24Ma92f8: JEE Main 2024 Mathematics - Class 11 JEEM24Ma92f8 Solution: Let be the circle of minimum area touching the parabola and the …

Let CC be the circle of minimum area touching the parabola y=6−x2y=6-x^2 and the lines y=3∣x∣y=\sqrt{3}|x| . Then, which one of the following points lies on the circle CC ?

Multiple Choice Options

  • A (1,2)(1,2)
  • B (2,2)(2,2)
  • C (1,1)(1,1)
  • D (2,4)(2,4)

Step-by-Step Verified Solution

Let centre be (0, k)

JEE Main 2024 (Online) 6th April Morning Shift Mathematics - Parabola Question 13 English Explanation

Now radius is r=6−kr=6-k

Also, 6−k=∣k2∣6-k=\left|\frac{k}{2}\right|

amp;⇒6−k=k2amp;⇒12−2k=kamp;⇒k=4\begin{aligned}& \Rightarrow 6-k=\frac{k}{2} \\& \Rightarrow 12-2 k=k \\& \Rightarrow k=4\end{aligned}

Radius, r=6−4=2r=6-4=2

So circle will be

amp;(x)2+(y−k)2=4amp;x2+(y−4)2=4\begin{aligned}& (x)^2+(y-k)^2=4 \\& x^2+(y-4)^2=4\end{aligned}

(2,4)(2,4) satisfies this equation.

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