(a) The stretch in the y-direction changes the distance from the center to the maximum point from 2 to 6 (since the maximum point is at 12 and the minimum at 0, the center is at 6). Therefore, the scale factor of the stretch is \(\frac{6}{2} = 3\).

(b) The radius of the original circle is the distance from the center to the maximum point before the stretch, which is 2.

(c) After the translation \(\begin{pmatrix} 7 \\ -3 \end{pmatrix}\), the center of the circle moves from (1, 5) to \((1+7, 5-3) = (8, 2)\).

(d) The original center of the circle is found by reversing the translation from (8, 2): \((8-7, 2+3) = (1, 5)\).