JEE Main 2025 — Parabola Questions with Solutions

Let the shortest distance from (a, 0), a0, to the parabola y²=4 x be 4 . Then the equation of the circle passing throug…

Two parabolas have the same focus (4,3) and their directrices are the x -axis and the y -axis, respectively. If these p…

Let A and B be the two points of intersection of the line y+5=0 and the mirror image of the parabola y²=4 x with respec…

If the equation of the parabola with vertex V ((3)/(2), 3 ) and the directrix x+2 y=0 is α x²+β y²-γ x y-30 x-60 y+225=…

Let P be the parabola, whose focus is (-2,1) and directrix is 2 x+y+2=0. Then the sum of the ordinates of the points on…

A line passing through the point A(-2,0), touches the parabola P: y²=x-2 at the point B in the first quadrant. The area…

Let the focal chord P Q of the parabola y²=4 x make an angle of 60ⁱrc with the positive x-axis, where P lies in the fir…

If the line 3 x-2 y+12=0 intersects the parabola 4 y=3 x² at the points A and B, then at the vertex of the parabola, th…

The axis of a parabola is the line y=x and its vertex and focus are in the first quadrant at distances √(2) and 2 √(2)…

Let P(4,4 √(3)) be a point on the parabola y²=4 a x and PQ be a focal chord of the parabola. If M and N are the foot of…