Conic Sections

JEE Main 2025 (Online) 22nd January Morning ShiftMCQMedium📈 Topic in 29% papers+4−1

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

Let the parabola y=x2+px-3, meet the coordinate axes at the points P, Q and R. If the circle C with centre at (-1,-1) passes through the points P, Q and R, then the area of PQR is :

Answer

(2) 6

Solution

The centre lies on the perpendicular bisector of chord PQ (on the x-axis): + 2=-1 p=2.

[figure]

x2+2x-3=0 P(1,0), Q(-3,0); R(0,-3)

Base PQ=4, height OR=3

Area = 12 4 3=6

Answer: (2)

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Ques. 2JEE 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

Ques. 3JEE 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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