unable to solve([x^2+y^2==4, (y-y0)^2+z^2==4], [x, y, z])

savecancel

here is the script:

x, y, z = var('x, y, z');
y0 = var('y0');
solve([x^2+y^2==4, (y-y0)^2+z^2==4], [x, y, z]);
[x^2 + y^2 == 4, (y - y0)^2 + z^2 == 4]

but if:

y0 = 0

solve([x^2+y^2==4, (y-y0)^2+z^2==4], [x, y, z]);

gives the expected answer:

[[x == r1, y == -sqrt(-r1^2 + 4), z == r13, [x == r2, y ==
sqrt(-r2^2 + 4), z == r2, [x == r3, y == -sqrt(-r3^2 + 4), z ==
-r3], [x == r4, y == sqrt(-r4^2 + 4), z == -r4]]

With parameter y0, I would expect:

[x = +- sqrt(4-u^2),
y = u,
z = +- sqrt(4-(u-y0)^2)]

Thank you for helping me.