Question

Find the distance between the directrices of the ellipse `x^2/36 + y^2/20` = 1

Answer 1

Given equation of ellipse is `x^2/36 + y^2/20` = 1

Here a² = 36

⇒ a = 6

b² = 20

⇒ b = `2sqrt(3)`

We know that b² = a²(1 – e²)

⇒ 20 = 36(1 – e²)

⇒ 1 – e² = `20/36`

⇒ e² = `1 - 20/36 = 16/36`

⇒ e = `4/6 = 2/3`

Now distance between the directrices is `a/e - (a/e)`

= `a/e + a/e = (2a)/`

= `2 xx 6/(2/3)`

= `2 xx 6 xx 3/2`

= 18

Hence, the required distance = 18.