At each point (x, y) of a curve, the intercept of the tangent on the y-axis is equal to $2 x y^{2}$ . Find the equation of the curve.

\frac{x}{y} = x^{2} + C

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\frac{y}{x} = y^{2} + C

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\frac{x}{y} = y^{2} + C

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{y}{x} = x^{2} + C

No worries! We‘ve got your back. Try BYJU‘S free classes today!

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Solution

The correct option is A $\frac{x}{y} = x^{2} + C$
The equation of tangent is
$y = m x + c$
We know that slope m = $\frac{d y}{d x}$
$y = \frac{d y}{d x} x + 2 x y^{2}$
$y d x - x d y = 2 x y^{2} d x$
$\frac{y d x - x d y}{y^{2}} = 2 x d x$
Integrate
$\frac{x}{y} = x^{2} + C$

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