JEE Main 2021 — Parabola Questions with Solutions

A tangent line L is drawn at the point 2 ,   - 4 on the parabola y 2 = 8 x . If the line L is also tangent to the…

If the three normals drawn to the parabola, y 2 = 2 x pass through the point a , 0 ,   a ≠ 0 , then a must b…

Let P be a variable point on the parabola y = 4 x 2 + 1 . Then, the locus of the mid-point of the point P and the foot…

A tangent is drawn to the parabola y 2 = 6 x which is perpendicular to the line 2 x + y = 1 . Which of the following po…

Consider the parabola with vertex 1 2 ,   3 4 and the directrix y = 1 2 . Let P be the point where the parabola me…

If a line along a chord of the circle 4 x 2 + 4 y 2 + 120 x + 675 = 0 , passes through the point ( - 30 , 0 ) and is ta…

Let C be the locus of the mirror image of a point on the parabola y 2 = 4 x with respect to the line y = x . Then the e…

Let y = m x + c , m > 0 be the focal chord of y 2 = - 64 x , which is tangent to ( x + 10 ) 2 + y 2 = 4 . Then, the…

If the point on the curve y 2 = 6 x , nearest to the point 3 , 3 2 is ( α , β ) , then 2 ( α + β )…

The length of the latus rectum of a parabola, whose vertex and focus are on the positive x -axis at a distance R and S…