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Answer to Question #2959 in Analytic Geometry for ZENGA

Question #2959
Find the intersection of the line X + Y - 6 = 0 and the circle X2 + Y2 - 4X - 4 = 0.
Expert's answer
We have to solve the system of equations:
X + Y -6 =0
X2 +Y2 - 4X -4 =0

X = 6-Y,
(6-Y)2 + Y2 - 4(6-Y) - 4 = 36 - 12Y + Y2 + Y2 - 24 + 4Y - 4 = 2Y2 - 8Y + 8
2Y2 - 8Y + 8 =0
Y2 - 4Y + 4 =0
(Y-2)2 = 0
Y = 2, X = 6-Y = 6-2 = 4.

Answer: the intersection point of the line and the circle is (4,2).

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