Question

Find the equation for the ellipse that satisfies the given conditions,
Ends fo major axis $(\pm 3,0)$ ends of minor axis $(0,\pm 2)$

Answer 1

Ends of major axis $(\pm 3,0)\text{lie on x. axis. So the equation of ellipse in standard form is},(\frac{x^2}{a^2}+\frac{y^2}{b^2})=1$
Now ends fo major axis $(\pm a,0)is(\pm 3,0)$
$\Rightarrow a=3$
Ends fo minor axis $(0,\pm b)is(0,\pm 2)\Rightarrow b=2$ Thus equation of required ellipse is,
$\frac{x^2}{9}+\frac{y^2}{4}=1.$