Question #2959

Find the intersection of the line X + Y - 6 = 0 and the circle X[sup]2[/sup] + Y[sup]2 [/sup]- 4X - 4 = 0.

Expert's answer

We have to solve the system of equations:

X + Y -6 =0

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

X = 6-Y,

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

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

Y^{2} - 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).

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).

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