Where does the normal line intersect the second time?

[UsernameValid]

Where does the normal line to the ellipse x²-xy+y²=3 at the point (-1,1) intersect the ellipse a second time?So I took the derivative of the equation to get:
y'=(2x-y)/(x-2y)
Then I put (-1,1) into the equation, to get a slope of 1.
So, for the normal line I got a slope of -1, which has the equation y=-x.

And that's as far as I got, I know the answer is suppose to be (1,-1).

 

[UsernameValid]

Nevermind, I figured it out.