creating series of arches off the tangent of another arch

Hi there, 

Very new to grasshopper, and was wondering if I could get some help on lining up some arches. 

I want a series of parabolic/catenary arches. The first arch is symmetrical and spans along a curve. I want the second arch to extend in the following directions: 

From the tangent at the vertex of the inner arch or, 

Continuing to extend at the same angle of the right inner arch. 

I have done some basic experimenting, however the arches that i have made do not meet at the same angle, which i i'm not sure if it would be structurally stable. 

Additionally, within my script my parabolic arches are two different arches joining together so i am uncertain whether they are symmetrical. How would i be able to create a catenary arch in this situation?

Thanks

Refeences:

My poor attempt at trying to join arches off the tangents:

Screenshot%20%28232%29.png

Another attempt

Screenshot%20%28231%29.png

14.08.15%20arch%20series_02.gh