Question

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

Solution

Correct option is

       

or   a2(1 – e2) = 9b2 = 9b2(1 – e2)

.

SIMILAR QUESTIONS

Q1

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

Q2

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

Q3

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

Q4

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.

Q5

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

Q6

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

Q7

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

Q8

If latus rectum of the ellipse  is equal to

Q9

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.

Q10

The eccentricity of the ellipse with its center at the origin is . If one of the directrices is x = 4, then the equation of the ellipse is