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(B) According to the given information,the slope of the curve at any point $(x, y)$ is given by $\frac{dy}{dx} = \frac{1}{2y}$.By separating the varia

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Parabola

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(B) According to the given information,the slope of the curve at any point $(x, y)$ is given by $\frac{dy}{dx} = \frac{1}{2y}$.By separating the variables,we get $2y \, dy = dx$.Integrating both sides,we have $\int 2y \, dy = \int dx$,which gives $y^2 = x + c$.Since the curve passes through the point $(3, 4)$,we substitute $x = 3$ and $y = 4$ into the equation: $4^2 = 3 + c$,which implies $16 = 3 + c$,so $c = 13$.Thus,the equation of the curve is $y^2 = x + 13$.This equation is of the form $y^2 = 4a(x - h)$,which represents a parabola.

If it is mentioned that for a curve passing through $(3,4)$,the slope of the curve at any point is the reciprocal of twice the ordinate of that point,then that curve is a

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