JEE Main 2025 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 3 April 2025, Shift 1, Maths Q11

Question 11 of 75 in this shift, Maths question 11 of 25, Section A.

The radius of the smallest circle which touches the parabolas

y = x^2 + 2

and

x = y^2 + 2

(1) $\frac{7\sqrt{2}}{2}$
(2) $\frac{7\sqrt{2}}{16}$
(3) $\frac{7\sqrt{2}}{4}$
(4) $\frac{7\sqrt{2}}{8}$ Official answer

Official answer

Option 4

NTA final key.

Chapter: Conic Sections
Topic: Normals to Conics
Idea tested: Shortest Distance via Common Normal

Same topic in other shifts

All Normals to Conics questions

27 Jan 2024, Shift 1 · Q10If the shortest distance of the parabola $y^2=4x$ from the centre of the circle $x^2+y^2-4x-16y+64=0$ is d, then $d^2$ is equal to :MediumSingle correct
11 Apr 2023, Shift 2 · Q27Let the tangent to the parabola $y^2 = 12x$ at the point $(3, \alpha)$ be perpendicular to the line $2x + 2y = 3$ . Then the square of…HardNumerical value
26 Jul 2022, Shift 1 · Q13Let the tangent drawn to the parabola $y^2 = 24x$ at the point $(\alpha,\ \beta)$ is perpendicular to the line $2x + 2y = 5$ . Then the…MediumSingle correct
26 Jul 2022, Shift 1 · Q29Let the function $f(x) = 2x^2 - \log_e x$ , $x > 0$ , be decreasing in $(0,\ \mathrm{a})$ and increasing in $(\mathrm{a},\ 4)$ . A tangent to…HardNumerical value
25 Jun 2022, Shift 2 · Q29Let the eccentricity of the hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$ be $\frac{5}{4}$ . If the equation of the normal at the point…HardNumerical value
26 Jun 2022, Shift 1 · Q13Let the normal at the point P on the parabola $y^2 = 6x$ pass through the point $(5, -8)$ . If the tangent at P to the parabola intersects…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 108 of the 174 JEE Main shifts held from 2017 to 2026.