Question

The equation of the ellipse having foci (0, 1), (0, –1) and minor axis of length 1 is ______. 

Answer 1

The equation of the ellipse having foci (0, 1), (0, –1) and minor axis of length 1 is `bbunderline((4x^2)/1 + (4y^2)/5 = 1)`.

Explanation:

We know that the foci of the ellipse are (0, ± ae)

And given foci are (0, ± 1)

So be = 1

Length of minor axis = 2b = 1

⇒ `b = 1/2`

We know that b² = a² (1 – e²)

⇒ `1/4 = a^2 - 1`

⇒ `a^1 = 1 + 1/4 = 5/4`

∴ Equation of ellipse is `x^2/b^2 + y^2/a^2` = 1

⇒ `x^2/(1/4) + y^2/(5/4)` = 1

⇒ `(4x^2)/1 + (4y^2)/5` = 1