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(C) Given that the slope of the curve is the reciprocal of twice the ordinate $(y)$: $\frac{dy}{dx} = \frac{1}{2y}$ By separating the variables,we get

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$y^2 = x + 5$

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(C) Given that the slope of the curve is the reciprocal of twice the ordinate $(y)$: $\frac{dy}{dx} = \frac{1}{2y}$ By separating the variables,we get: $2y \, dy = dx$ Integrating both sides: $\int 2y \, dy = \int dx$ $y^2 = x + C$ Since the curve passes through the point $(4, 3)$,we substitute $x = 4$ and $y = 3$: $3^2 = 4 + C$ $9 = 4 + C$ $C = 5$ Substituting the value of $C$ back into the equation,we get: $y^2 = x + 5$

The slope of a curve at any point is the reciprocal of twice the ordinate at the point and it passes through the point $(4, 3)$. The equation of the curve is

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