Question

( 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} )

# 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

Solution