Question

The differential equation of all parabolas whose axes are parallel to $y$ -axis is:

• A. $\frac{d^{3}y}{d{x}^3}=0$
• B. $\frac{d^{2}x}{d{y}^2}=0$
• C. $\frac{d^{3}y}{d{x}^3}+\frac{d^{2}y}{d{x}^2}=0$
• D. $\frac{d^{2}y}{d{x}^2}+2\frac{dy}{dx}=0$

Answer 1

The correct option is A $\frac{d^{3}y}{d{x}^3}=0$

Equation of parabola is $(x-h{)}^2=4a(y-k)$

Differentiating w.r.t. x, we get,

$\Rightarrow 2(x-h)=4a{y}_1$

$\Rightarrow (x-h)=2a{y}_1$

$\Rightarrow 1=2a{y}_2$

$\Rightarrow y_2=\frac{1}{2a}$

Differentiating w.r.t. x, we get,

$\Rightarrow y_3=0$

$\Rightarrow \frac{d^{3}y}{d{x}^3}=0$