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  4. The curve passing through the point (1, 2) given that the slope of the tangent at any point (x, y) is (2x/y) represents

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Q. The curve passing through the point $(1, 2)$ given that the slope of the tangent at any point $(x, y)$ is $\frac{2x}{y}$ represents

KCETKCET 2020

Solution:

Given, $\left(\frac{dy}{dx}= \frac{2x}{y}\right)$
$\Rightarrow y d y=2 x d x$
$\Rightarrow \int y d y=\int 2 x d x$
$\Rightarrow y^{2} / 2=x^{2}+A$, where $A$ is a constant.
The above equation represents a hyperbola.