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Friday, 9 October

JEE Main 2022 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 29 June 2022, Shift 1, Maths Q18

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

Let PQ be a focal chord of the parabola y2=4xy^2 = 4x such that it subtends an angle of π2\frac{\pi}{2} at the point (3,0)(3, 0). Let the line segment PQ be also a focal chord of the ellipse E:x2a2+y2b2=1E: \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1, a2>b2a^2 > b^2. If ee is the eccentricity of the ellipse E, then the value of 1e2\frac{1}{e^2} is equal to :
  1. (1)1+21 + \sqrt{2}
  2. (2)3+223 + 2\sqrt{2}Official answer
  3. (3)1+231 + 2\sqrt{3}
  4. (4)4+534 + 5\sqrt{3}

Official answer

Option 2

NTA final key (2022 Session 1).

Chapter
Conic Sections
Topic
Parabola Focal Chords
Idea tested
Equation of focal chord

Same topic in other shifts

All Parabola Focal Chords questions
  1. 5 Apr 2026, Shift 2 · Q12Let the directrix of the parabola P:y2=8xP: y^2=8x, cut x-axis at the point A. Let B(α,β)B(\alpha, \beta), α>1\alpha>1, be a point on P such that…MediumSingle correct
  2. 2 Apr 2025, Shift 1 · Q1Let the focal chord PQ of the parabola y2=4xy^2=4x make an angle of 60∘60^\circ with the positive xx-axis, where P lies in the first…MediumSingle correct
  3. 2 Apr 2025, Shift 2 · Q11Let the point PP of the focal chord PQPQ of the parabola y2=16xy^2 = 16x be (1,−4)(1, -4). If the focus of the parabola divides the chord PQPQ in…MediumSingle correct
  4. 9 Jan 2020, Shift 2 · Q66If one end of a focal chord AB of the parabola y2=8xy^2=8x is at A(12,−2)A\left(\frac{1}{2},-2\right), then the equation of the tangent to it at B…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 42 of the 174 JEE Main shifts held from 2017 to 2026.