Question

The degree and order of the differential equation of the family of all those parabola's whose axis is $x$-axis are respectively.

• A. 1, 2
• B. 3, 2
• C. 2, 3
• D. 2, 1

Answer 1

The correct option is A 1, 2

Equation of the required parabola is of the form $y^2=4a(x-h)$.
Differentiating we have
$2y\frac{dy}{dx}=4a\Rightarrow y\frac{dy}{dx}=2a\Rightarrow {\left(\frac{dy}{dx}\right)}^2+y\frac{d^{2}y}{d{x}^2}=0$
The degree of this differential equation is $1$ and the order is $2$.