Question

A focus of an ellipse is at the origin. The directrix is the line  x = 4 and the eccentricity is 1/2. Then the length of the semi-major axis, is  

Solution

Correct option is

8/3

 

Let the length of semi-major and semi-minor axes be a and brespectively  

We have, 

Distance between focus and directrix = 4. 

.

SIMILAR QUESTIONS

Q1

, then the chord joining two points θ1 and θ2 on the ellipse  will subtend a right angle at

Q2

The locus of the point of intersection of tangents to an ellipse at two points, sum of whose eccentric angles is constant is a/an

Q3

The number of values of c such that the straight line y = 4x + ctouches the curve , is  

Q4

, then PF1 + PF2 equals

Q5

An ellipse slides between two perpendicular straight lines. Then, the locus of its centre is a/an

Q6

The sum of the squares of the perpendicular on any tangent to the ellipse  from two points on the minor axis, each at a distance  from the centre is 

Q7

The eccentric angle of a point on the ellipse  whose distance from the centre of the ellipse is 2, is

Q8

If any tangent to the ellipse  intercepts equal length lon the axes, then =

Q9

The ellipse x2 + 4y2 = 4 is inscribed in a rectangle aligned with the coordinate axes, which in turn is inscribed in another ellipse that passes through the point (4, 0). Then, the equation of the ellipse is  

Q10

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