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$Orthogonal trajectories of family of the curve x^{\frac{2}{3}} + y^{\frac{2}{3}} = a^{\frac{2}{3}}, whose ' a' is an arbitrary constant is$

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x2/3-y2/3=c

x4/3-y4/3=c

x4/3+y4/3=c

x1/3-y1/3=c

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detailed solution

Correct option is B

23x-13+23y-13dydx=0→dydx=-y13x13 Replace dydx by −dxdy∴dxdy=y13x13⇒∫x13dx=∫y13dy⇒x43−y43=c

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Orthogonal trajectories of family of the curve x23+y23=a23 , whose ' a ' is an arbitrary constant is

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$Orthogonal trajectories of family of the curve x^{\frac{2}{3}} + y^{\frac{2}{3}} = a^{\frac{2}{3}}, whose ' a' is an arbitrary constant is$