What are the steps to solving this problem? (Thank you in advance)
Find the slope of the normal line to the curve (x^2)-(xy)+(y^2) = 7 at the point where x=1. There are two possible answers – accept the SMALLER answer.
Where I started:
y' = (y-2x) / (2y-x)
Best Answer
As $x^2 - xy + y^2 =7$, by differentiating w.r.t $x$,
$2x - xy' - y + 2yy' = 0$
and $$-\frac{1}{y'} = -\frac{x-2y}{2x-y}$$
At $x=1$, $1 -y+y^2 = 7 \implies y^2 -y -6 = 0\implies y = 3,-2$
At $(1,3)$ the slope is,
At $(1,-2)$,