JEE Main 2024 — Parabola Questions with Solutions

Consider the circle C: x²+y²=4 and the parabola P: y²=8 x. If the set of all values of α, for which three chords of the…

Let a conic C pass through the point (4,-2) and P(x, y), x ≥ 3, be any point on C. Let the slope of the line touching t…

Suppose A B is a focal chord of the parabola y²=12 x of length l and slope m < √(3). If the distance of the chord AB fr…

Let L₁, L₂ be the lines passing through the point P(0,1) and touching the parabola 9 x²+12 x+18 y-14=0. Let Q and R be…

Let PQ be a chord of the parabola y²=12 x and the midpoint of PQ be at (4,1). Then, which of the following point lies o…

The maximum area of a triangle whose one vertex is at ( 0 , 0 ) and the other two vertices lie on the curve y = - 2 x 2…

If the shortest distance of the parabola y 2 = 4 x from the centre of the circle x 2 + y 2 - 4 x - 16 y + 64 = 0 is d ,…

Let P ( α , β ) be a point on the parabola y 2 = 4 x . If P also lies on the chord of the parabola x 2 = 8 y whose mid…

Let the length of the focal chord PQ of the parabola y²=12 x be 15 units. If the distance of PQ from the origin is p, t…

Let a line perpendicular to the line 2 x-y=10 touch the parabola y²=4(x-9) at the point P. The distance of the point P…