A tangent and a normal are drawn at the point P(16, 16) of the parabola y2 = 16x which cut the axis of the parabola at the points A and B respectively. If the center of the circle through P, A and B is C, then angle between PC and axis of x is


Correct option is

a = 4, the point (16, 16) corresponds to (at2, 2at) for t = 2.

                 ty = x + at2

is tangent and y = –tx + 2at + at3 is normal. Putting y = 0, we get

A(– at2, 0) = (–16, 0), B(2a + 2t2, 0) = (24, 0)

The circle through A, B, P will be on AB as diameter as

. Hence center C is mid-point of AB is (4, 0).




If x + y = k is normal to y2 = 12x, then k is


A circle drawn on any focal chord AB of the parabola y2 = 4axas diameter cuts the parabola again at and D. If the parameters of the points A, B, C, D be t1, t2 t3 and t1 respectively, then the value of t3 t4 is


The length of normal chord which subtends an angle of 900 at the vertex of the parabola y2 = 4x is


A focal chord of parabola y2 = 4x is inclined at an angle of  with the +ive direction of x-axis, then the slope of normal drawn at the ends of focal chord will satisfy the equation


If two different tangents of y2 = 4x are the normal’s to the parabola x2 = 4ay, then


Find the locus of the mid-points of the chord of the parabola y2 = 4ax which subtend a right angle at the vertex.


If the parabola C and D intersect at a point A on the line L1, then equation of the tangent point L at A to the parabola D is


If a > 0, the angle subtended by the chord AB at the vertex of the parabola is


P is a point on the circle C, the perpendicular PQ to the major axis of the ellipse E meets the ellipse at M, then  is equal to