$C = \{(c_1,c_2):c_1^2 + c_2^2 \leq 1 \}$
$G = \{(g_1,g_2): g_1 = a_1 + d_1, g_2 = a_2 + d_2, d_1^2 + d_2^2 \leq 1 \}$
C is a unit circle centered at the origin, and G is a unit circle centered at $(a_1, a_2)$.
Define:
$X = \{(x_1,x_2): x_1 = c_1 g_1, x_2 = c_2 g_2, (c_1,c_2)\in C, (g_1, g_2)\in G\} $
What is the shape of $X$? Is there any name of it, or any other method to express like a polynomial equation? I thought it might be a ellipse or a circle, but it seems not.