Axis Constrained Collision Distance

[dotails]

View attachment 2237
I have 2 curves and I need to slide 1 of the circles along an axis until it exactly meets the other circle. How do I determine the distance until contact?

 

[Ackbach]

Draw a line from the center of the larger circle in the direction of its travel. You need to know the perpendicular-line distance from the center of the smaller circle to the drawn line. It is impossible to solve the problem without some information along those lines.