A conic satisfies the differential equation and passes through the point

MATHEMATICS · Single correct · CBSE · Mathematics · Differential Equations · Differential Equations

Problem

A conic

C

satisfies the differential equation

(1+y^2)\,dx-xy\,dy=0

and passes through the point

(1,0)

. An ellipse

E

is confocal with

C

and has eccentricity

\sqrt{\frac{2}{3}}

. Find the equation of the ellipse

E

. (1)

\frac{x^2}{3}+\frac{y^2}{1}=1

(2)

\frac{x^2}{1}+\frac{y^2}{3}=1

(3)

\frac{x^2}{4}+\frac{y^2}{9}=1

(4)

\frac{x^2}{9}+\frac{y^2}{4}=1