The two curves x3−3xy2+2=0  and 3x2y−y3−2=0 intersect at an angle of whose degree measure is  

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

intersect at an angle of whose degree measure is  

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    Solution:

    For the curve x3-3xy2+2=0, the gradient is dydx=-3x2-3y2-6xy=x2-y22xy

    For the curve 3x2yy32=0, the gradient is dydx=-6xy3x2-3y2=-2xyx2-y2

    Observing the above two gradients, the product of slopes is -1

    hence, the angle between the curves is 900

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