JEE Main · 2008 · 27 Apr 2008 · Offline · Ellipse

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

Answer: (A)

Solution

With a focus at the origin and the corresponding directrix at

x = 4

, the distance from the centre to the directrix is

\frac{a}{e}

and to the focus is

a e

, and their difference is the focus-to-directrix distance of

4

. So

\frac{a}{e} - a e = 4

, and with

e = \frac{1}{2}

this is

a (2 - \frac{1}{2}) = \frac{3 a}{2} = 4

, giving

a = \frac{8}{3}

for the semi-major axis.

JEE Main · 2008 · 27 Apr 2008 · Offline · Single correct option