There are two railroads, represented by the curves y=(1/2)x2+7, and x2+y2=1. I am supposed to find a straight line connection so that a atrain can get from one curve to the other. I have drawn a simple diagram to help me picture things: http://i50.tinypic.com/2saeccx.png where (a,b) and (c,d) will be the points at which the line will connect with each curve. I've found the derivatives to the curves to be y'=x and y'=-x/y respectively. I understand that these give me the slopes of the tangent lines for each curve, so would I be correct in reasoning that x=-x/y since the slopes should be the same?