Q.

Let slope of the tangent line to a curve at any point P(x,y) be given by xy2+yx . If the  curve intersects the line x+2y=4 at x=-2, then the value of y, for which the point (3,y) lies on the curve, is :

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a

(3,y) lies on the curve, is :

b

−43

c

1835

d

−1819

answer is D.

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Detailed Solution

dydx=xy2+yx  xdy-ydx=xy2dxydx-xdyy2=-xdx⇒∫dxy=fxdx⇒xy=-x22+c↓ passes through (-2,3)⇒-23=-2+c⇒c=43 Curve is xy=-x22+43(3,y) lies on it ⇒3y=-92+43⇒3y=-196⇒y=-1819
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Let slope of the tangent line to a curve at any point P(x,y) be given by xy2+yx . If the  curve intersects the line x+2y=4 at x=-2, then the value of y, for which the point (3,y) lies on the curve, is :