Question

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

Solution

Correct option is

         y2 = ax                          … (1)

Tangent any point (x1y1) is

      

or  ax – 2yy1 + ax1 = 0        ... (2)

But (1) y2 = ax its any tangent is

           

Here, 

       4x – 4y + = 0        … (3)

Compare (1) and (2),

  

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SIMILAR QUESTIONS

Q1

A point moves on the parabola y2 = 4ax. Its distance from the focus is minimum for the following value(s) of x.

Q2

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

Q3

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

Q4

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

Q5

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

Q6

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

Q7

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

Q8

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

Q9

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

Q10

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