Question

The differential equation of all parabolas whose directrices are parallel to the x-axis is

• A. $\frac{d^{3}y}{dx^{3}}$ = 0
• B. $\frac{d^{3}x}{dy^{3}}$ = 0
• C. $\frac{d^{3}y}{dx^{3} + \frac{d^{2}y}{dx^{2}}}$ = 0
• D. None of these

Answer 1

Answer: (A)

$\frac{d^{3}y}{dx^{3}}$ = 0

Answer 2

The equation of family is y = Ax² + Bx + C, where A, B, C are arbitrary constants. Hence, $\frac{d^{3}y}{dx^{3}}$ = 0