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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

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

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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.
answered Feb 5, 2014 by meena.p
 

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