Graph problem

I'm having a little problem with the equation for a graph. I'm looking for something where the line is completely horizontal at point 1,1 and completely vertical at 0,0. So far I have y=-x^2+2x which gives a horizontal line at 1,1, but not a vertical line at point 0,0 - I don't think it can be done with a parabola, but I have no idea where to go from here. Pardon my noobishness. Some help please?

(x-1)^2 + y^2 = 1

Differentiate

2(x - 1) + 2y (dy/dx) = 0

dy/dx = 2(1 - x) / 2y

dy/dx @ 1,1 = 0/2 = Horizontal

dy/dx @ 0,0 = 2/0 = Vertical

All he said he needed was an equation, not a function. (x - 1)^2 + y^2 = 1 works.