How do I find the normals to the curve
xy+ 2x - y = 0 that are parallel to the line 2x + y = 0
If the normals are parallel to
2x + y = 0 where the slope is -2, the tangent to the curve is (-1)(1/(-2)=1/2.
given
xy+ 2x - y = 0
y=2x/(1-x)
y' = 2/(x^2-2*x+1)
Solve for x in
y'=1/2, or
2/(x^2-2*x+1)=1/2
I get x=3 or x=-1.