Question

Find the equation of the ellipse in the cases given below:

Length of latus rectum 4, distance between foci `4sqrt(2)`, centre (0, 0) and major axis as y-axis

Answer 1

Given `(2"b"^2)/"a"` = 4 and 2ae = `4sqrt(2)`

Now `(2"b"^2)/"a"` = 4

2b² = 4a

⇒ b² = 2a

2ae = `4sqrt(2)`

ae = `sqrt(2)`

So a²e² = 4(2) = 8

We know b² = a²(1 – e²)

= a² – a²e²

⇒ 2a = a² – 8

⇒ a² – 2a – 8 = 0

⇒ (a – 4)(a +2) = 0

⇒ a = 4 or – 2

As a cannot be negative

a = 4

So a² = 16 and b² = 2(4) = 8

Also major axis is along j-axis

So equation of ellipse is `x^2/8 + y^2/16` = 1