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Question

The two curves x33xy2+2=0 and 3x2yy32=0


A

Cut at right angles

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B

Touch each other

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C

Cut at an angle π/3

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D

Cut at an angle π/4

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Solution

The correct option is A

Cut at right angles


x33xy2+2=0...(1)3x2yy32=0...(2)
On differentiating equations (1) and (2) w.r.t x, we obtain
(dydx)c1=x2y22xy and (dydx)c2=2xyx2y2
Since m1.m2=1.Therefore the two curves cut at right angles.
Hence (a) is the correct answer.

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