Question

Find the locus of the point of intersection of the tangents to the ellipse , if the difference of the eccentric angle of their points of contact is 2α.

Solution

Correct option is

Let the point of intersection be (h, k). Let θ1 and θ2 be the eccentric angles such that

       θ1 – θ2 = 2α                      … (1)

Points of contacts are  and the equations of tangents at these points are

       

Since these tangents pass through (h, k)

         

On solving these equations, we get

     

  

.

SIMILAR QUESTIONS

Q1

If  is a tangent to the ellipse , then find out the eccentric angle of the point of tangency.

Q2

For what value of λ dose the line y = x + λ touches the ellipse 9x2 + 16y2 = 144.

Q3

Find the equations of the tangents to the ellipse 3x2 + 4y2 = 12 which perpendicular to the line y + 2x = 4.

Q4

Find the equation of pair of tangents drawn from the point (1, 2) and (2, 1) to the ellipse .

Q5

A tangent to the circle x2 + y= 5 at the point (–2, 1) intersect the ellipse  at the point A, B. If tangents to the ellipse at the point A and B intersect at point C. Find the coordinate of points C.

Q6

If the line 3y = 3x + 1 is a normal to the ellipse , then find out the length of the minor axis of the ellipse.

Q7

If SK be the perpendicular from the focus S on the tangent at any point P on the ellipse , then locus of K is 

Q8

The tangent and normal to the ellipse x2 + 4y2 = 4 at a point P(θ) in second quadrant, meet the major axis in Q and R respectively. If QR = 2, then cos θ is equal to

Q9

If latus rectum of the ellipse  is equal to

Q10

In an ellipse, the distance between its foci is 6 and minor axis 8. The eccentricity of the ellipse is