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
x3 = y
Differentiating on both sides with respect to x, we get
so from equation (i) and (ii), we get
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.