1. Given the equation of the rotated ellipse x^2+xy+y^2=3

a. Find the equation of the normal line (line perpendicular to the tangent line at the given point) to it at x=1

I got 2 points for the problem (1,1) and (1,-2) but you just need one of the normal line. So I did dy/dx=-3y-2x. I picked (1,1) which gives me dy/dx=-5 so the slope of the normal line is 1/5 and the equation of the line would be y-1=(1/5)(x-1). Can someone check my work- I think I'm doing something wrong for some reason.

b. Find the second point on the curve where the normal line is parallel to the one you found in part (a).

I have no idea how to attempt this problem.

c. Find the point(s) on the curve where the tangent line is vertical.

Kinda lost on this problem also...

Thanks!