The slope of a curve at any point is inversel | vedclass

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Question

(C) Given that the slope $\frac{dy}{dx}$ is inversely proportional to $2y$,we have: $\frac{dy}{dx} = \frac{1}{2y}$ Separating the variables,we get: $2

Vedclass · Accepted Answer

$y^2 = x + 5$

Vedclass · Answer

(C) Given that the slope $\frac{dy}{dx}$ is inversely proportional to $2y$,we have: $\frac{dy}{dx} = \frac{1}{2y}$ 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 $(4, 3)$,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 inversely proportional to twice the $y$-coordinate of that point. If the curve passes through $(4, 3)$,then the equation of the curve is:

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