Stones Dropped into a Calm Pond at Points a and B

Multiple Choice

Stones dropped into a calm pond at points A and B create ripples that propagate in widening circles.In the figure below, points A and B are 12 feet apart, and the radii of the circles differ by 4 feet.The point
P (x, y) where the circles intersect moves along a curve.Find the equation of the curve.

A) $\quad \frac { ( x - 4 ) ^ { 2 } } { 4 } - \frac { ( y - 4 ) ^ { 2 } } { 32 } = 1$
B) $\quad \frac { x ^ { 2 } } { 4 } - \frac { y ^ { 2 } } { 32 } = 1$
C) $\quad \frac { x ^ { 2 } } { 6 } + \frac { y ^ { 2 } } { 64 } = 1$
D) $\quad \frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 32 } = 1$
E) none of these