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Parabola — BITSAT Mathematics PYQs

17 previous year questions from Parabola with answers and solutions. Numbered list, year tags, and one-tap solutions — built for serious JEE / NEET practice.

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Parabola — BITSAT Mathematics PYQs

If the focus of parabola (y-k)^2=4(x-h) always lies between the lines x+y=1 and x+y=3 then

Let L₁ be the length of the common chord of the curves x^2+y^2=9 and y^2=8 x , and L₂ be the length of the latus rectum of y^2=8 x , then:

If vertex of a parabola is (2,-1) and the equation of its directrix is 4 x-3 y=21 , then the length of its latus rectum is

The equation of a common tangent to the parabolas y=x^2 and y=-(x-2)^2 is

If the straight line y=m x+c touches the parabola y^2-4 a x+4 a^3=0 , then c is

A normal is drawn at the point P to the parabola y^2=8 x , which is inclined at 60^ with the straight line y=8 . Then the point P lies on the straight line

The length of the latus rectum of the parabola which has focus at (-1,1) and the directrix is 4 x +3 y-24=0 is

Suppose a parabola y = a x 2 + b x + c has two x intercepts, one positive and one negative, and its vertex is ( 2 , - 2 ) , then which of the following is true?

Normals drawn to y 2 = 4 a x at the points where it is intersected by the line y = m x + c intersected at P . Coordinates of foot of the another normal drawn to the parabola from t

The locus of the point of intersection of two tangents to the parabola y²=4 a x, which are at right angle to one another is

The parabola having its focus at (3,2) and directrix along the y -axis has its vertex at

Let S be the focus of the parabola y ²=8 x and PQ be the common chord of the circle x ²+ y ²-2 x -4 y=0 and the given parabola. The area of P Q S is

Through the vertex O of a parabola y ²=4 x , chords OP and O Q are drawn at right angles to one another. The locus of the middle point of PQ is

If the line 2 x -3 y = k touches the parabola y ²=6 x , then find the value of k

The length of the latus-rectum of the parabola whose focus is ( ( u^2 2 g 2 ,- u^2 2 g 2 ) ) and directrix is (y= u^2 2 g ), is

If the equations of the pairs of opposite sides of a parallelogram are (x^2-5 x+6=0 ) and (y^2-6 y+5=0 ), then equations of its diagonals are

The line (3 x-4 y+7=0 ) is rotated through an angle ( 4 ) in the clockwise direction about the point ((-1,1) ). The equation of the line in its new position is