A) cut at right angles
B) touch each other
C) cut at an angle\[\frac{\pi }{3}\]
D) cut at an angle\[\frac{\pi }{4}\]
Correct Answer: A
Solution :
We have\[{{x}^{3}}-3x{{y}^{2}}+2=0\] ...(i) and \[3{{x}^{2}}y-{{y}^{3}}-2=0\] ...(ii) Diff. equation (i) and (ii) with respect to\[x,\]we obtain \[{{\left( \frac{dy}{dx} \right)}_{{{C}_{1}}}}=\frac{{{x}^{2}}-{{y}^{2}}}{2xy}\]and\[{{\left( \frac{dy}{dx} \right)}_{C2}}=\frac{-2xy}{{{x}^{2}}-{{y}^{2}}}\] \[{{m}_{1}}\times {{m}_{2}}=-1\] Hence, the two curves cut at right angles.
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