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Saturday, 31 October

JEE Main 2022 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 29 July 2022, Shift 1, Maths Q17

Question 17 of 90 in this shift, Maths question 17 of 30, Section A.

Let the focal chord of the parabola P:y2=4xP : y^2 = 4x along the line L:y=mx+cL : y = mx + c, m>0m > 0 meet the parabola at the points M and N. Let the line L be a tangent to the hyperbola H:x2−y2=4H : x^2 - y^2 = 4. If O is the vertex of P and F is the focus of H on the positive xx-axis, then the area of the quadrilateral OMFN is :
  1. (1)262\sqrt{6}
  2. (2)2142\sqrt{14}Official answer
  3. (3)464\sqrt{6}
  4. (4)4144\sqrt{14}

Official answer

Option 2

NTA final key.

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

Same idea in other shifts

Asked 3× in all
  1. 8 Apr 2023, Shift 1 · Q14Let RR be the focus of the parabola y2=20xy^2=20x and the line y=mx+cy=mx+c intersect the parabola at two points PP and QQ. Let the point…HardSingle correct
  2. 29 Jun 2022, Shift 1 · Q18Let 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…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.