Differential EquationHard

Question

The differential equation of all parabola having their axis of symmetry coinciding with the x-axis is

Options

A.
B.
C.
D.none of these

Solution

    
Directrix ⊥ to x axis, Let x = α  and focus on x axis Let (β,0) , Now
(x - β)2 + y2 = (x - α)2   
β2 - 2βx + y2 = α2 - 2αx                                 
y2 = 2(β - α) x + α2 - β2               
In general    y2 = mx + c   (Two arbitnary constant m and c)
2y = m

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