find the differential equation of all parabola with x axis and (a,0) as focus
Answer (1)
17th Jan, 2021
Hello,
As the parabola is parallel to x axis with focus at a,0. Hence the equation of such parabola is given as:
y^2 = 4ax
Now to make the differential equation, we have to remove the a from this. So differentiate this equation one time wrt. x, because there is only one arbitrary constant.
2y .dy/dx = 4a
Now put this value of 4a in the upper equation we get the differential equation i.e.
y^2 - 2xy. dy/dx = 0
Hope it helps.
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