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+1 vote
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in Derivatives by (50.2k points)
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If the curve ay + x2 = 7 and x3 = y, cut orthogonally at (1, 1), then the value of a is:

A. 1
B. 0
C. – 6
D. 6

1 Answer

+1 vote
by (48.8k points)
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Best answer

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.

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