Question

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

Solution

Correct option is

Any tangent to parabola y2 = 4x , (a = 1)

                                     … (1)

Now any normal to parabola x2 = 4ay is

      x = My – 2aM – aM3                    … (2)

or                   … (3)

If (1) and (3) are same, then

     

or  aM2 – M + 2a = 0

If will have two real rots if 1 – 8a2 > 0

or  .

SIMILAR QUESTIONS

Q1

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

Q2

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

Q3

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

Q4

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

Q5

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

Q6

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

Q7

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

Q8

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

Q9

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

Q10

Equation of the diameter of the ellipse conjugate to the diameter respected by L is