If C is at (0,0), then the condition:
x2/a2 + y2/b2 = 1
will be true for all points on the ellipse.
So for a given x:
y2/b2 = 1 - x2/a2
y2 = (1 - x2/a2) * b2
y = +/- sqrt((1 - x2/a2) * b2)
where +/- means that y can have two values, +... and -...., and sqrt is the square root (?0.5)
You could also calculate the ellipse based on:
r1 + r2 = 2(a-c) + 2c = 2a