JEE Main 2022 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 28 June 2022, Shift 1, Maths Q14

Question 14 of 90 in this shift, Maths question 14 of 30, Section A.

If the tangents drawn at the points O(0, 0) and P

\left(1+\sqrt{5}, 2\right)

on the circle

x^2+y^2-2x-4y=0

intersect at the point Q, then the area of the triangle OPQ is equal to

(1) $\frac{3+\sqrt{5}}{2}$
(2) $\frac{4+2\sqrt{5}}{2}$
(3) $\frac{5+3\sqrt{5}}{2}$ Official answer
(4) $\frac{7+3\sqrt{5}}{2}$

Official answer

Option 3

NTA final key.

Chapter: Conic Sections
Topic: Circle Tangents
Idea tested: Area of Tangent-Chord Triangle

Same idea in other shifts

Asked 5× in all

28 Jul 2022, Shift 2 · Q73Let the tangents at two points A and B on the circle $x^2+y^2-4x+3=0$ meet at origin O (0, 0). Then the area of the triangle OAB is :MediumSingle correct
29 Jun 2022, Shift 1 · Q19Let the tangent to the circle $C_1: x^2 + y^2 = 2$ at the point $M(-1, 1)$ intersect the circle $C_2: (x - 3)^2 + (y - 2)^2 = 5$ , at two…HardSingle correct
31 Aug 2021, Shift 2 · Q88Let B be the centre of the circle $x^2+y^2-2x+4y+1 = 0$ . Let the tangents at two points P and Q on the circle intersect at the point…HardNumerical value
17 Mar 2021, Shift 2 · Q78Two tangents are drawn from a point P to the circle $x^2+y^2-2x-4y+4=0$ , such that the angle between these tangents is…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.