Question

The angle between the tangents drawn from the origin to the parabola y2 = 4a(x – a) is

Solution

Correct option is

900

Any line through origin is y = mx,. Since it is a tangent to

    y2 = 4a(x – a), it will cut it in two coincident points.

  Roots of m2x2 – 4ax + 4a2 are equal  

  16a2 – 16a2m2 = 0  or m2 = 1

or  m = 1, –1.

Product of slopes = –1

Hence a right angle.

SIMILAR QUESTIONS

Q1

If the line x – 1 = 0 is the directrix of the parabola y– ky + 8 = 0, then one of the of the value of k is

  

Q2

Equation of the parabola whose axis is y = x distance from origin to vertex is  and distance form origin to focus is , is (Focus and vertex lie in Ist quadrant) :

Q3

The focal chord of y2 = 16x is tangent to (x – 6)2 + y2 = 2, then the possible values of the slope of this chord, are

Q4

The curve described parametrically by x = t2 + t + 1, y = t2 – + 1 represents.

Q5

The locus of the mid-point of the line segment joining the focus to a moving point on the parabola y2 = 4ax is another parabola with directrix

Q6

If  and the line 2bx + 3cy + 4d = 0 passes through the points of intersection of the parabolas y2 = 4ax and x2 = 4ay, then

   

Q7

Let P be the point (1, 0) and Q a point on the locus y2 = 8x. The locus of mid-point of PQ is

Q8

Consider the two curves C1 : y2 = 4xC2 : x2 + y2 – 6x + 1 = 0. Then,

Q9

Angle between tangents drawn from the point (1, 4) to the parabola y2 = 4is

Q10

 

The equation of the common tangent touching the circle (x – 3)2 + y2 = 9 and the parabola y2 = 4x above the x-axis is