The degree and order of differential equation of family of parabolas whose length of latus rectum is fixed and axis is x-axis ,are respectively

Question

$(a)\;(2,3) \\ (b)\;(1,2) \\ (c)\;(2,1) \\ (d)\;(3,2) $

Answer 1

equation can be $(y-k)^2 =a(x-h) \quad a=fixed.$

differentiating this we get,

$2(y-k).y'=ax$

$(y-k).y''+y'^2=\large\frac{a}{2}$

$\large\frac{ax}{2y'}.y''+y'^2=\large\frac{a}{2}$

$ax.y''+2y'^3=ay'$

order =2

degree =1

Hence b is the correct answer.