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(A) The general equation of a parabola whose axis of symmetry is along the $X$-axis is given by $y^2 = 4a(x - h)$, which can be rewritten as $y^2 = Ax

Vedclass · Accepted Answer

$2$

Vedclass · Answer

(A) The general equation of a parabola whose axis of symmetry is along the $X$-axis is given by $y^2 = 4a(x - h)$, which can be rewritten as $y^2 = Ax + B$, where $A$ and $B$ are arbitrary constants.Since there are $2$ arbitrary constants, we need to differentiate the equation twice to eliminate them.First derivative: $2y \frac{dy}{dx} = A$.Second derivative: $2 \left( \left( \frac{dy}{dx} \right)^2 + y \frac{d^2y}{dx^2} \right) = 0$.Since the highest order derivative present in the differential equation is the second derivative, the order of the differential equation is $2$.

The order of the differential equation of all parabolas whose axis of symmetry is along the $X$-axis is:

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