Assertion (A): The differential equation representing the family of parabolas y^2=4 ax, where ‘a’ is a parameter, is x dy/dx-2 y =0. Reason (R): If…

Assertion (A): The differential equation representing the family of parabolas $\displaystyle \mathrm{y}^2=4 \mathrm{ax}$, where ‘a’ is a parameter, is $\displaystyle \mathrm{x} \frac{\mathrm{dy}}{\mathrm{dx}}-2 \mathrm{y}=0$. Reason (R): If the given family of curves has n parameters, then it is to be differentiated n times to eliminate the parameter and obtain the $\displaystyle \mathrm{n}^{\text {th }}$ order differential equation.