+937 I tried to graph all 3, but how would you know where they intersect, at one point ot two points without a calc?
+129850 Set the circles equal
(x - 3)^2 + (y - 4)^2 = (x + 4)^2 + (y - 3)^2
x^2 - 6x + 9 + y^2 - 8y + 16 = x^2 + 8x + 16 + y^2 -6y + 9
-6x - 8y = 8x - 6y
-2y = 14x
y = -7x
Sub this into (x - 3)^2 + (y - 4)^2 = 25
(x - 3)^2 + ( -7x - 4)^2 = 25
x^2 - 6x + 9 + 49x^2 + 56x + 16 = 25
50x^2 + 50x + 25 = 25
x ( x + 1) = 0
x = 0 or x = -1
So....the intersection of the circles will occur at (0,0) and (-1, 7)
Find the intersection of (x - 3)^2 + ( y - 4)^2 = 25 and y = - 6x
(x - 3)^2 + ( -6x - 4) = 25
x^2 - 6x + 9 + 36x^2 + 48x + 16 = 25
37x^2 + 42x = 0
x (37x + 42) = 0
x = 0 or x = -42/37
Putting these into y = -6x
(0, 0) and (-42/37, 252/37)
And find the intersection of (x +4)^2 + ( y - 3)^2 = 25 and y = - 6x
(x + 4)^2 + (-6x - 3)^2 = 25
x^2 + 8x + 16 + 36x^2 + 36x = 9 = 25
37x^2 + 44x = 0
x (37x + 44) = 0
x = 0 or x = -44/37
Putting these into y = -6x
(0, 0) and ( -44/37, 264/37)
Note that (0,0 ) will satisfy all three
But only (-1, 7) ( -42/37, 252/37) and (-44/37, 264/37) will satisfy two of the three
Answer: 3
