Eclipse problem... need explanation please

Question

The graph of the equation x^2 y^2 = 169 includes how many points (x,y) in the coordinate plane where x and y are both negative integers.

Please explain...

Answer 1

x^2 + y^2 = 169

is a circle of radius 13 centred at (0, 0).

Starting from the diameter point (- 13, 0), try all successive integers from - 12 to 0 for x, and find whether the corresponding y value is a perfect square. The only two points with neither co-ordinate zero are (- 12, - 5) and (- 5, - 12).