curious how to program a conic arc

I'm not exactly sure how to express a hyperbolic or elliptical arc in linuxcnc, though I am certain that it can be done. I just don't know where to start exactly, any help would be appreciated.

Hi. Do you have the math that descrines the arc you intend to cut?

I do, 7.5mm radius with a Rho value of 0.3

Ok, so without resorting to CAM, there are two methods that I can think of now.
1. Use a repeat subroutine (o100 repeat [nn], o100 endrepeat). Use G1 and increment x with each cycle and calculate y based on the new x value using variables (# parameters). Note that certain # parameters are local (1-30) and wont work in subroutines.
2. Use Excel or similar to calculate the x,y coordinates and use a G1 from point to point.

Well, I'm not sure why I didn't think about linking x and y with an equation...

Ideally I'm going for a subroutine with as few input variables as possible, I think I may have it figured. Fetch the current position, relate to finished position and calculate mid point, use midway point, radius, and Rho value to establish a scaling off the line between the two points, generating a curve

I am not sure if it helps (in fact it probably doesn't) But LinuxCNC can work in polar coordinates if you want.

linuxcnc.org/docs/html/gcode/overview.html#_polar_coordinates

And can also do quadratic splines, cubic splines and NURBS:
linuxcnc.org/docs/2.7/html/gcode/g-code.html#gcode:g5