MHT CET 2026 Mathematics question

The differential equation of the family of all parabolas whose axis is the -axis is ...

(A)
(B)Correct
(C)
(D)

Answer: (B)

Solution

A parabola whose axis is the -axis has its vertex on the -axis, so the family is , with two arbitrary constants and , hence the differential equation is of order 2. Differentiate once: , i.e. . Differentiate again: , so

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Question ID VK-100351