The two curves x2 – 3xy2 + 2 = 0 an...
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The two curves x2 – 3xy2 + 2 = 0 and 3xły – y3 –2 = 0 (a) cut at right angles (b) touch each other (c) cut at an angle (d) cut at an angle

JEE/Engineering Exams
Maths
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( C_{1}: x^{3}-3 x y^{2}+2=0 ) ( 3 x^{2}-3 y^{2}-3 x(2 y) d y=0 ) ( Rightarrow quad 3left(x^{2}-y^{2}right)=6 x y frac{d y}{d x} ) ( Rightarrow frac{d y}{d x}=frac{x^{2}-y^{2}}{2 x y} ) Slope of tangut at ( Pleft(x, y_{1}right)=frac{x_{1}^{2}-y_{1}^{2}}{2 x_{1} y_{1}}=m_{1} ) ( N_{0 w}, m_{1} m_{2}=left(frac{x_{1}^{2}-y_{1}^{2}}{2 x_{1} y_{1}}right)left(frac{-2 x_{1} y_{1}}{x_{1}^{2}-y_{1}^{2}}right)=-1 ) ( Rightarrow ) thyserts to the wirve, ( G ) & ( C_{2} ) cut each otheer at ( 90^{circ} ) at point of intersection option ( (a) ) ( Rightarrow ) both mive cut each other at ( 90^{circ} )
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