find the equation of the ellipse in the following cases:
Length of minor axis 16 foci (0, ± 6)
Given that we need to find the equation of the ellipse whose length of the minor axis is 16 and foci (0,±6).
Let us assume the equation of the ellipse as (b2>a2).
We know that the length of the minor axis of the ellipse is 2a,
⇒ 2a = 16
⇒ a = 8
⇒ a2 = 64
We know that foci = (0,±be)
⇒ be = 6
We know that eccentricity
⇒
⇒ 36 = b2 - 64
⇒ b2 = 100
The equation of the ellipse is
⇒
∴ The equation of the ellipse is .