Question

The order of the differential equation of all parabolas, whose latus rectum is $4a$ and axis parallel to the x-axis, is

• A. one
• B. four
• C. three
• D. two

Answer 1

The correct option is D two

The equation of the parabolas whose length of the latus rectum is $4a$ and its axis is paralell to x-axis is,

${(y-k)}^2=4a(x-h)$,

Here $4a$ is a constant and the parameters are $h$ and $k$,

Therefore the order of the differential equation is $2$,

$2(y-k)\frac{dy}{dx}=4a⟹2a\frac{d^{2}y}{d{x}^2}+{\left(\frac{dy}{dx}\right)}^2=0$