Question

Find the equation for the ellipse that satisfies the given conditions,
Foci $(\pm 3,0)a=4$

Answer 1

The foci $(\pm 3,0)$ lie on x - axis.
So the equation of ellipse in standard form is,
$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$
$\text{Now foci}(\pm c,0)\text{is}(\pm 3,0)\Rightarrow c=3\text{We know that}{c}^2=a^2-b^2\therefore (3{)}^2=(4{)}^2-b^2\Rightarrow b^2=16-9=7$
Thus equation of required ellipse is,
$\frac{x^2}{16}+\frac{y^2}{7}=1.$