Find the equation of the ellipse whose vertices are the (0, ±4) and foci at .
Given: Vertices = (0, ±4) …(i)
The vertices are of the form = (0, ±a) …(ii)
Hence, the major axis is along y – axis
∴ From eq. (i) and (ii), we get
a = 4
⇒ a2 = 16
and We know that, if the major axis is along y – axis then the equation of Ellipse is of the form of
Also, given coordinate of foci = (0, ±√7) …(iii)
We know that,
Coordinates of foci = (0, ±c) …(iv)
∴ From eq. (iii) and (iv), we get
c = √7
We know that,
c2 = a2 – b2
⇒ (√7)2 = (4)2 – b2
⇒ 7 = 16 – b2
⇒ b2 = 16 – 7
⇒ b2 = 9
Substituting the value of a2 and b2 in the equation of an ellipse, we get