Question

The order and degree of the differential equation of parabolas having vertex at the origin and focus at (a, 0) where a > 0, are respectively:

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

Answer 1

The correct option is B 2, 1

Equation of parabola having vertex at the origin and focus at $(a,0)$ , where $a>0$ is $y^2=4ax$

On differentiating the above equation, we get

$2y\frac{dy}{dx}=4a$

or, $y\frac{dy}{dx}=2a$

or, $y\frac{d^{2}y}{d{x}^2}+{\left(\frac{dy}{dx}\right)}^2=0$

Hence, order and degree of differential equation are $2$ and $1$ respectively.

Hence, B is the correct option.