Question

The differential equation of the family of ellipses with centre at the origin and the ends of the major axis being $\left(\pm 1,0\right)$ is of the degree

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

Answer: (A)

The general equation of the family is $x^2+\frac{y^2}{a^2}=1\dots \dots ..\left(i\right)$
Differentiating w.r.t. $x,$ we get $2x+\frac{2y{y}^{{}^{\prime }}}{a^2}=0$
$\Rightarrow x=-\frac{y^{{}^{\prime }}y}{a^2}\Rightarrow a^2=-\frac{y^{{}^{\prime }}}{x}$
Putting in (i), we have $x^2+y^2\left(-\frac{x}{y{y}^{{}^{\prime }}}\right)=1$
or $x^2-\frac{xy}{y^{{}^{\prime }}}=1$
Which is of the degree ${}^{\prime }{1}^{\prime }$