Question

Find the equation for the ellipse that satisfies the given conditions,
Length of minor axis 16, foci $(0,\pm 6)$

Answer 1

The foci $(0,\pm 6)$ lie on y - axis.
So the equation of ellipse in standard form is,
$\frac{x^2}{b^2}+\frac{y^2}{a^2}=1\text{Now length of minor axis}2b=16\Rightarrow b=8\text{foci}(0,\pm c)\text{is}(0,\pm 6)\Rightarrow c=6\text{We know that}{c}^2=a^2-b^2$
$\therefore (6{)}^2=a^2-(8{)}^2\Rightarrow a^2=36+64=100\text{Thus equation of required ellipse is},\frac{x^2}{64}+\frac{y^2}{100}=1$