Question

Find the equation for the ellipse that satisfies the given conditions :

Length of minor axis 16, foci = (0, $\pm$6)

Answer 1

Length of minor axis = 16

Foci = (0, $\pm$ 6)

Since, the foci are on the y-axis, the major axis is along the y-axis.

Therefore, the equation of ellipse will be of the form $\frac{x^2}{b^2}+\frac{y^2}{a^2}=1$, where a is the semi major axis.

Accordingly,

$2b=16⟹b=8$

$c=6$

It is known that $a^2=b^2+c^2$

Therefore, $a^2=100$

$a=10$

Thus, the equation of the ellipse is

$\frac{x^2}{64}+\frac{y^2}{100}=1$