Find the equation of the ellipse whose foci are at (±1, 0) and .
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