Question

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