Circle And System Of Circles Question 295

Question: The equation of the circumcircle of the triangle formed by the lines $ y+\sqrt{3}x=6,\ y-\sqrt{3}x=6, $ and $ y=0 $ , is

[EAMCET 1982]

Options:

A) $ x^{2}+y^{2}-4y=0 $

B) $ x^{2}+y^{2}+4x=0 $

C) $ x^{2}+y^{2}-4y=12 $

D) $ x^{2}+y^{2}+4x=12 $

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Answer:

Correct Answer: C

Solution:

Solving $ y=0 $ and $ y+\sqrt{3}x=6 $ , we get $ (2\sqrt{3},,0) $ , only option (c) satisfies the co-ordinate.