JEE Main 2020 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 6 September 2020, Shift 2, Maths Q65

Question 65 of 75 in this shift, Maths question 15 of 25.

The centre of the circle passing through the point

(0,1)

and touching the parabola

y=x^2

at the point

(2,4)

is :

(1) $\left(\frac{-53}{10},\frac{16}{5}\right)$
(2) $\left(\frac{3}{10},\frac{16}{5}\right)$
(3) $\left(\frac{-16}{5},\frac{53}{10}\right)$ Official answer
(4) $\left(\frac{6}{5},\frac{53}{10}\right)$

Official answer

Option 3

NTA final key (Sep 2020).

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
4 Aug 2021, Shift 1 · Q73Consider 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…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

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.