Question

Two tangent are drawn from the point (–2, –1) to the parabola y2 = 4x. if  is the angle between them, then 

Solution

Correct option is

3

                y2 = 4x                … (1)

Writing  S = y2 – 4x, T = yy1 – 2(x + x1)

             S = 1 + 8 = 9    T = –y – 2(x – 2)

                = –(2x + y – 4)

Pair of tangents through (–2, –1) is SS1 = T2

(y2 – 4x)9 = (2x + y – 4)2

 4x2 – 8y2 + 20x – 8+ 4xy = 0

                  = ax2 + 2hxy + by2 + 2gx + 2fy

If  is angle between pair of tangents, then

        

SIMILAR QUESTIONS

Q1

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

Q2

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

Q3

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

Q4

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

Q5

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

Q6

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

Q7

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

Q8

The angle of intersection between the curves y2 = 4x and x2 = 32y at point (16, 8) is

Q9

The pole of the line lx + mx + n = 0 with respect to the parabola y2 = 4ax is

Q10

The conic represented by the equation  is