"Complete the square for x : "Complete the square for x :
"(x+3)^2 + y^2 = 13(x+3)2+y2=13
"As both terms are positive, we know that"As both terms are positive, we know that
-4 < x+3 < 4−4<x+3<4
"and"and
-4 < y < 4−4<y<4
y = pm 3 => x+3 = pm 2 => x = -5 or -1y=±3⇒x+3=±2⇒x=−5or−1
y = pm 2 => x+3 = pm 3 => x = -6 or 0y=±2⇒x+3=±3⇒x=−6or0
y = pm 1 " and " y = 0, " yield no perfect square"y=±1 and y=0, yield no perfect square
"So we have 8 solutions : "So we have 8 solutions :
(-5, -3), (-5, 3), (-1, -3), (-1, 3),(−5,−3),(−5,3),(−1,−3),(−1,3),
(-6, -2), (-6, 2), (0, -2), (0, 2).(−6,−2),(−6,2),(0,−2),(0,2).