Proof a set is affine, a cone, a convex set

Question

I just met a problem when proving if a set is affine, a cone or a convex set.

$S = \{a∈R^2 | a_1x_1+a_2x_2≤2, x_1^2+x_2^2≤1，∀x∈R^2\}$.

Following the definitions, to see if it is affine, I have to check if $λa+(1-λ)b ∈S$,

then I got $(λa+(1-λ)b)x_1+(λa+(1-λ)b)x_2$,

I want to conclude that since $a∈R^2$, then $(λa+(1-λ)b)∈R^2$。

I'm not sure if I can draw such a conclusion. And similar to the proof of cone, I check if $λa$ is in $S$, then it goes similar as above.

Can anyone help clarify my confusion? Thanks!