Question

Find the equation for the ellipse that satisfies the given conditions,
Vertices $(\pm 5,0),Foci(\pm 4,0)$

Answer 1

The Foci $(\pm 4,0)$ lie on x - axis.
So the equation of ellipse in standard form is,
$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$
Now vertices $(\pm a,0)is(\pm 5,0)\Rightarrow a=5$
$\text{Foci}(\pm c,0)\text{is}(\pm 4,0)\Rightarrow c=4\text{We know that}{c}^2=a^2-b^2\therefore (4{)}^2=(5{)}^2-b^2\Rightarrow b^2=25-16=9$
Thus equation of required ellipse is,
$\frac{x^2}{25}+\frac{y^2}{9}=1.$