If a curve passes through the point -2-3 and has slope 2 x-v2 at any point x- y on it- then the point on the curve where abscissa is 2 is

The correct option is C 3Given dy/dx=2x/y^2 ⇒ y^2 dy=2xdx ⇒y^3/3=x^2+C Since curve passing through ( 2, 3) ⇒27/3=4+C⇒ c=5 ∴ equation of curve y^3/3=x^2+5 Wh ...

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Standard XII

Chemistry

Rate of Reaction

If a curve pa...

Question

If a curve passes through the point (-2, 3) and has slope $\frac{2 x}{y^{2}}$ at any point (x, y) on it, then the point on the curve where abscissa is 2 is ___

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Solution

The correct option is C 3
Given $\frac{d y}{d x} = \frac{2 x}{y^{2}}$
$\Rightarrow y^{2} d y = 2 x d x$
$\Rightarrow \frac{y^{3}}{3} = x^{2} + C$
Since curve passing through (-2, 3)
$\Rightarrow \frac{27}{3} = 4 + C \Rightarrow c = 5$
$∴$ equation of curve $\frac{y^{3}}{3} = x^{2} + 5$
When x = 2, y = 3

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If a curve passes through the point (-2, 3) and has slope 2xy2 at any point (x, y) on it, then the point on the curve where abscissa is 2 is ___

The correct option is C 3Given dydx=2xy2 ⇒y2dy=2xdx ⇒y33=x2+C Since curve passing through (-2, 3) ⇒273=4+C⇒c=5 ∴ equation of curve y33=x2+5 When x = 2, y = 3

If a curve passes through the point (-2, 3) and has slope $\frac{2 x}{y^{2}}$ at any point (x, y) on it, then the point on the curve where abscissa is 2 is ___