Q. 18

Find the equation

Answer :

Let the equation of the required ellipse be

Given:

Coordinates of foci = (±1, 0) …(i)

We know that,

Coordinates of foci = (±c, 0) …(ii)

∴ From eq. (i) and (ii), we get

c = 1

It is also given that

we know that,

[∵ c = 1]

⇒ a = 2

Now, we know that,

c² = a² – b²

⇒ (1)² = (2)² – b²

⇒ 1 = 4 – b²

⇒ b² = 4 – 1

⇒ b² = 3

Substituting the value of a² and b² in the equation of an ellipse, we get

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