Question

If the curve $ay+x^2=7$, and $x^3=y$ cut orthogonally at $(1,1)$, then the value of $a$ is

• A. $1$
• B. $0$
• C. $-6$
• D. $6$

Answer 1

The correct option is D $6$

Slope of the tangent at $(1,1)$ to $ay+x^2=7$ is $m_1=-\frac{2}{a}$.

Slope of the tangent at $(1,1)$ to $x^3=y$ is $m_2=3$.

$\because$ Curves cuts orthogonally, $m_1\times m_2=-1$

$\therefore m_1\times m_2=-\frac{2}{a}.3=-1$
$\therefore a=6$