Conic Sections

JEE Main 2025 (Online) 22nd January Evening ShiftMCQMedium📈 Topic in 50% papers+4−1

Ques. 1JEE Main 2025, 22 January (Evening Shift)

Let P(4,4 3) be a point on the parabola y2=4ax and PQ be a focal chord of the parabola. If M and N are the foot of perpendiculars drawn from P and Q respectively on the directrix of the parabola, then the area of the quadrilateral PQMN is equal to :

34 33
343 38
17 3
263 38

Answer

(2) 343 38

Solution

P(4,4 3) on y2=4ax a=3: y2=12x, focus S(3,0), directrix x=-3

P=(3t2,6t), t1= 2 3; focal chord t1t2=-1 Q= ( 94,-3 3 )

[figure]

PM QN (both horizontal) trapezium: PM=7, QN= 214, height MN=7 3

Area = 12 494 7 3= 343 38

Answer: (2)

Keep practising — Conic Sections

Ques. 2JEE Main 2025, 22 January (Evening Shift)

Let E: x2a2+ y2b2=1, a>b and H: x2A2- y2B2=1. Let the distance between the foci of E and the foci of H be 2 3. If a-A=2, and the ratio of the eccentricities of E and H is 13, then the sum of the lengths of their latus rectums is equal to :

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