The order and degree of the differential equation of all the parabolas which have a fixed length of latus rectum and their axes are parallel to the x -axis, are respectively

Step-by-step solution

Let, the length of the latus rectum is 4 a , then the equation of such family of parabolas is y - k 2 = 4 a x - h , where, h , k are arbitrary constants On differentiating, we get, 2 y - k d y d x = 4 a … 1 y - k d 2 y d x 2 + d y d x 2 = 0 … 2 From 1 putting the value of y - k , we get, 2 a d y d x d 2 y d x 2 + d y d x 2 = 0 2 a d 2 y d x 2 + d y d x 3 = 0 Hence, order = 2 , degree = 1