If the curve ay + x2 = 7 and x3 = y, cut orthogonally at (1, 1), then the value of a is:


Given the curve ay + x2 = 7 and x3 = y, cut orthogonally at (1, 1),

ay + x2 = 7


Differentiating on both sides with respect to x, we get



Applying the sum rule of differentiation and also the derivative of the constant is 0, so we get



Applying the power rule we get




The value of above derivative at (1,1), becomes




x3 = y


Differentiating on both sides with respect to x, we get



Applying the power rule we get



The value of above derivative at (1,1), becomes




Now as these two curves cut orthogonally at (1,1), so



so from equation (i) and (ii), we get




a=6


Hence f the curve ay + x2 = 7 and x3 = y, cut orthogonally at (1, 1), then the value of a is 6.


So the correct option is option D.

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