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

Category: QuestionsWhat is the differential equation of all parabolas whose directrices are parallel to the x-axis?
Editor">Editor Staff asked 11 months ago

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
 
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Origin of the question is Linear Second Order Differential Equations in portion Differential Equations of Mathematics – Class 12
NCERT Solutions for Subject Clas 12 Math Select the correct answer from above options 
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1 Answers
Editor">Editor Staff answered 11 months ago

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