# Answer to Question #2959 in Analytic Geometry for ZENGA

Question #2959

Find the intersection of the line X + Y - 6 = 0 and the circle X

^{2}+ Y^{2 }- 4X - 4 = 0.Expert's answer

We have to solve the system of equations:

X + Y -6 =0

X

X = 6-Y,

(6-Y)

2Y

Y

(Y-2)

Y = 2, X = 6-Y = 6-2 = 4.

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

X + Y -6 =0

X

^{2}+Y^{2}- 4X -4 =0X = 6-Y,

(6-Y)

^{2}+ Y^{2}- 4(6-Y) - 4 = 36 - 12Y + Y^{2}+ Y^{2}- 24 + 4Y - 4 = 2Y^{2}- 8Y + 82Y

^{2}- 8Y + 8 =0Y

^{2}- 4Y + 4 =0(Y-2)

^{2}= 0Y = 2, X = 6-Y = 6-2 = 4.

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

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