Question

find the eccentricity of an ellipse whose latus rectum is quarter of its major axis?​

Answer 1

Given: Latus rectum is quarter of its major axis.

To find: The eccentricity of an ellipse.

Solution:

• Let the equation of ellipse be x²/a² + y²/b² = 1 where a>b.

• If eccentricity is e, then it would be:

               b² = a²(1-e²) .................(i)

• Now the major axis is 2a.

• Length of latus rectum is 2b²/a²

• Now we have given that:

           length of LR = 1/4 x Length of major axis.

           2b²/a² = 1/4 x a

           2( a²(1-e²)) /a = 1/4 x a ................from (i)

           (1-e²)= 1/8

           1 - 1/8 = e²

           7/8 = e²

           e = √7/8

Answer:

              So the eccentricity of an ellipse is √7/8