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Saturday, 31 October

JEE Main 2021 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 17 March 2021, Shift 2, Maths Q78

Question 78 of 90 in this shift, Maths question 18 of 30, Section A.

Two tangents are drawn from a point P to the circle x2+y2−2x−4y+4=0x^2+y^2-2x-4y+4=0, such that the angle between these tangents is tan⁡−1(125)\tan^{-1}\left(\frac{12}{5}\right), where tan⁡−1(125)∈(0,π)\tan^{-1}\left(\frac{12}{5}\right)\in(0, \pi). If the centre of the circle is denoted by C and these tangents touch the circle at points A and B, then the ratio of the areas of Δ\DeltaPAB and Δ\DeltaCAB is :
  1. (1)9:49 : 4Official answer
  2. (2)3:13 : 1
  3. (3)2:12 : 1
  4. (4)11:411 : 4

Official answer

Option 1

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
  1. 28 Jul 2022, Shift 2 · Q73Let the tangents at two points A and B on the circle x2+y2−4x+3=0x^2+y^2-4x+3=0 meet at origin O (0, 0). Then the area of the triangle OAB is :MediumSingle correct
  2. 28 Jun 2022, Shift 1 · Q14If the tangents drawn at the points O(0, 0) and P(1+5,2)\left(1+\sqrt{5}, 2\right) on the circle x2+y2−2x−4y=0x^2+y^2-2x-4y=0 intersect at the point Q,…MediumSingle correct
  3. 29 Jun 2022, Shift 1 · Q19Let the tangent to the circle C1:x2+y2=2C_1: x^2 + y^2 = 2 at the point M(−1,1)M(-1, 1) intersect the circle C2:(x−3)2+(y−2)2=5C_2: (x - 3)^2 + (y - 2)^2 = 5, at two…HardSingle correct
  4. 31 Aug 2021, Shift 2 · Q88Let B be the centre of the circle x2+y2−2x+4y+1=0x^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

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.