Question

Find the equation of the ellipse in standard form if: the distance between its directrices is 10 and which passes through (-√5, 2). 

Answer 1

 Let the required equation of ellipse be \(\frac {x^2}{a^2} + \frac {y^2}{b^2} = 1\) where a > b.

Distance between directrices = 2a/e

Given, distance between directrices = 10

2a/e = 10

a = 5e …..(i) 

The ellipse passes through (-√5, 2). 

Substituting x = -√5 and y = 2 in equation of ellipse, we get

\(\frac {\sqrt5)^2}{a^2} + \frac {2^2}{b^2} = 1\)

b² = 6

The required equation of ellipse is \(\frac {x^2}{15} + \frac {y^2}{6} =1\)