# Where does the normal line intersect the second time?

1. Nov 14, 2012

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).

2. Nov 14, 2012