JEE Main 2021 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 4 August 2021, Shift 1, Maths Q73

Question 73 of 90 in this shift, Maths question 13 of 30, Section A.

Consider a family of circles which pass through the point

(1, 1)

and touch the axis of

y

. If the centre of such a circle is at

(h, k)

, then the set of all values of

h

is the interval

(1) $\left[\frac{1}{2},\infty\right)$ Official answer
(2) $\left[\frac{1}{4},\infty\right)$
(3) $\left(0,\frac{1}{2}\right)$
(4) $\left[\frac{1}{2},1\right]$

Official answer

Option 1

NTA final key.

Chapter: Conic Sections
Topic: Circle Tangents
Idea tested: Family of Circles Touching a Line

Same idea in other shifts

Asked 8× in all

6 Apr 2026, Shift 2 · Q10Let C be a circle having centre in the first quadrant and touching the $x$ -axis at a distance of 3 units from the origin. If the circle C…MediumSingle correct
2 Apr 2025, Shift 1 · Q22The absolute difference between the squares of the radii of the two circles passing through the point $(-9, 4)$ and touching the lines…HardNumerical value
25 Jul 2022, Shift 1 · Q29The sum of diameters of the circles that touch (i) the parabola $75x^2=64(5y-3)$ at the point $\left(\frac{8}{5},\frac{6}{5}\right)$ and…HardNumerical value
24 Jun 2022, Shift 2 · Q27Let a circle $C : (x-h)^2 + (y-k)^2 = r^2$ , $k > 0$ , touch the $x$ -axis at $(1, 0)$ . If the line $x + y = 0$ intersects the circle $C$ at…MediumNumerical value
25 Jun 2022, Shift 1 · Q1Let a circle C touch the lines $\mathrm{L_1}$ : $4x-3y+K_1=0$ and $\mathrm{L_2}$ : $4x-3y+K_2=0$ , $K_1, K_2 \in \mathbf{R}$ . If a line…MediumSingle correct
26 Aug 2021, Shift 2 · Q71A circle C touches the line $x=2y$ at the point $(2,\ 1)$ and intersects the circle $C_1:x^2+y^2+2y-5=0$ at two points P and Q such that…HardSingle correct
6 Sep 2020, Shift 2 · Q65The centre of the circle passing through the point $(0,1)$ and touching the parabola $y=x^2$ at the point $(2,4)$ is :HardSingle 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.