Question

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

(a) d^3x/dy^3 = 0

(b) d^3y/(dx^3 + d^2y/dx^2) = 0

(c) d^3y/dx^3 = 0

(d) d^2y/dx^2 = 0

I have been asked this question in an online interview.

Origin of the question is Linear Second Order Differential Equations in portion Differential Equations of Mathematics – Class 12

Answer 1

Right answer is (c) d^3y/dx^3 = 0

To explain I would say: The equation of family of parabolas is Ax^2 + Bx + C = 0 where, A, B, C are arbitrary constant.

By differentiating the equation with respect to x till all the constants get eliminated,

Hence, d^3y/dx^3 = 0