What is degrevlex?

Use e.g.

G:=Basis(K, 'tord', variables={r,u,v,w}); tord;

You could define the polynomial functions and use the composition operator @.

Or, better, use subs.
Notice first that the degrees of a and b must be 1.

a:=a1*x+a0;
                           a1 x + a0
b:=b1*x+b0;
                           b1 x + b0
c:=subs(x=a,b);
                      b1 (a1 x + a0) + b0
coeffs(collect(c-x,x),x):
sol:=solve([%],[a0,a1,b0,b1]):

# So, the general form of a,b is

{'a','b'} = eval({a,b},op(sol)); 

           {a,b} = {x/b1+a0, -a0*b1+b1*x}

# here a0,b1 are arbitrary constants, b1<>0.

Edit: actually c computes b o a, but the final result is of course the same. 

> min(extrema(x,{x^2 + x*y + y^2 = 2}));

It's a bug.

It seems that Apolonius works correctly only if all the 8 circles exist.