Question

Find the equation for the ellipse that satisfies the given conditions,
$\text{Vertices}(\pm 6,0),\text{foci}(\pm 4,0)$

Answer 1

The foci $(\pm 4,0)$ lie on x - axis.
So the equation of ellipse in standard form is,
$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$
$\text{Now vertices}(\pm a,0)\text{is}(\pm 6,0)\Rightarrow a=6\text{Foci}(\pm c,0)\text{is}(\pm 4,0)\Rightarrow c=4\text{We know that}{c}^2=a^2-b^2\therefore (4{)}^2=(6{)}^2-(b{)}^2\Rightarrow b^2=36-16=20\text{Thus equation of required ellipse is},\frac{x^2}{36}+\frac{y^2}{20}=1$