The differential equation of all parabolas ha | vedclass

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Question

(A) The general equation of a parabola with its axis of symmetry as the $x$-axis is given by $y^2 = 4a(x - h)$.Here,$a$ and $h$ are two arbitrary cons

Vedclass · Accepted Answer

$(2, 1)$

Vedclass · Answer

(A) The general equation of a parabola with its axis of symmetry as the $x$-axis is given by $y^2 = 4a(x - h)$.Here,$a$ and $h$ are two arbitrary constants.To form the differential equation,we differentiate with respect to $x$:$2y \frac{dy}{dx} = 4a$$y \frac{dy}{dx} = 2a$Differentiating again with respect to $x$:$y \frac{d^2y}{dx^2} + \left( \frac{dy}{dx} \right)^2 = 0$The highest order derivative present is $\frac{d^2y}{dx^2}$,so the order is $2$.The power of the highest order derivative is $1$,so the degree is $1$.Thus,the order and degree are $(2, 1)$.

The differential equation of all parabolas having their axis of symmetry coinciding with the $x$-axis has its order and degree respectively:

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