If the curve `a y+x^2=7` and `x^3=y` cut orthogonally at `(1,\ 1)` , then `a` is equal to (a) 1 (b) -6 (c) 6 (d) 0

Explanation

Slope of the tangent at (1,1) to `ay+x^2=7 `is `m_1​=−2/a`
​.
Slope of the tangent at (1,1) to `x^3=y` is` m_2​=3`
.

∵ Curves cuts orthogonally,

`m_1​×m_2​=−1`

∴`m_1​×m_2​`=−2/a​.3=−1`

∴a=6