Question

The differential equation of all parabolas each of which has a latus rectum ' $4a^{\prime }\&$ whose axes are parallel to $x$-axis is :

• A. of order $1\&$ degree 2
• B. of order $2\&$ degree 3
• C. of order 2 and degree 1
• D. of order 2 and degree 2

Answer 1

Answer: (C)

Equation to the family of parabolas is $(y-k{)}^2=4a(x-h)$
$2(y-k)\frac{dy}{dx}=4a\Rightarrow (y-k)\frac{dy}{dx}=2a$
$(y-k)\frac{d^{2}y}{d{x}^2}+{\left(\frac{dy}{dx}\right)}^2=0$
$2a\frac{d^{2}y}{d{x}^2}+{\left(\frac{dy}{dx}\right)}^3=0$.
Hence order is 2 and degree is 1 .