JEE Main 2024 · MathsMultiple choiceSingle correctMediumCalculation

JEE Main 27 January 2024, Shift 1, Maths Q10

Question 10 of 90 in this shift, Maths question 10 of 30, Section A.

If 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 :

(1) $16$
(2) $20$ Official answer
(3) $24$
(4) $36$

Official answer

Option 2

NTA final key.

Chapter: Conic Sections
Topic: Normals to Conics
Idea tested: Shortest Distance from Point to Parabola

Same topic in other shifts

All Normals to Conics questions

3 Apr 2025, Shift 1 · Q11The radius of the smallest circle which touches the parabolas $y = x^2 + 2$ and $x = y^2 + 2$ isHardSingle 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.