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 $x^{2}+\frac{y^{2}}{a^{2}}=1\ldots \ldots ..\left(i\right)$
Differentiating w.r.t. $x,$ we get $2x+\frac{2 y y^{'}}{a^{2}}=0$
$\Rightarrow x = - \frac{y^{'} y}{a^{2}} \Rightarrow a^{2} = - \frac{y^{'}}{x}$
Putting in (i), we have $x^{2} + y^{2} \left(- \frac{x}{y y^{'}}\right) = 1$
or $x^{2} - \frac{x y}{y^{'}} = 1$
Which is of the degree $'1'$