The points of intersection of $xy = 12$ and $x^2 + y^2 = 25$ are joined in succession. The resulting figure is: 
$\textbf{(A)}\ \text{a straight line}\qquad \textbf{(B)}\ \text{an equilateral triangle}\qquad \textbf{(C)}\ \text{a parallelogram} \\ \textbf{(D)}\ \text{a rectangle} \qquad \textbf{(E)}\ \text{a square}$
Graphing both equations, we see that the graphs intersect at $(-4, -3),$ $(-3, -4),$ $(3, 4),$ and $(4, 3).$ These points form a rectangle, so the answer is $\boxed{\textbf{(D)}}.$
~coolmath34