Question

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

Options

• 5

• 6

• 7

• 8

Answer 1

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

Explanation:

ay + x² = 7 and x³ = y cuts orthogonally.

Now `(dy/dx) = -(2x)/a` and `(dy/dx)` = 3x²

or `[(-(2x)/a)(3x^2)]_((1"," 1))` = –1

or `-2/3 xx 3` = –1 or a = 6.