Question

If a normal drawn to the parabola y2 = 4ax at the point (a, 2a) meets parabola again on (at2, 2at), then the value of t will be

Solution

Correct option is

–3

Given    y2 = 4ax                           … (1)

P(a, 2a), Q(at2, 2at)

(1)  

Equation of normal at P is

    

 x + y = 3a, it passes through Q(at2, 2at)

  at2 + 2at = 3a   t = 1, –3

But t = 1 correspond to point P,

    t = –3 is only required value.

SIMILAR QUESTIONS

Q1

The line x – y + 2 = 0 touches the parabola y2 = 8x at the point

Q2

If t is the parameter for one end of a focal chord of the parabola y2 = 4ax, then its length is

Q3

The point on the parabola y2 = 8x at which the normal is inclined at 600 to the x-axis has the coordinates

Q4

The length of the latus rectum of the parabola 9x2 – 6x + 36y + 19 = 0 is

Q5

The equation of a circle passing through the vertex the extremities of the latus rectum of the parabola y2 = 8x  is

Q6

If the parabola y2 = 4ax passes through the pint (1, –2), then the tangent at this point is

Q7

The equation of normal at the point  to the parabola y2 = 4ax, is

Q8

The equation of tangent at the point (1, 2) to the parabola y2 = 4ax, is

Q9

If a tangent of y2 = ax made angle of 450 with the x-axis, then its point of contact will be

Q10

If the straight line x + y = 1 touches the parabola y2 – y + x = 0, then the coordinates of the point of contact are