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Question
Find the equation of the circle which circumscribes the triangle formed by the lines
x + y = 2, 3x − 4y = 6 and x − y = 0.
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Solution
In \[∆\]ABC:
Let AB represent the line x + y = 2. ...(1)
Let BC represent the line 3x − 4y = 6. ...(2)
Let CA represent the line x − y = 0. ...(3)
Intersection point of (1) and (3) is (1, 1).
Intersection point of (1) and (2) is (2, 0).
Intersection point of (2) and (3) is (−6, −6).
The coordinates of A, B and C are (1, 1), (2, 0) and (−6, −6), respectively.
Let the equation of the circumcircle be
It passes through A, B and C.
∴ \[2 + 2g + 2f + c = 0\]
Hence, the required equation of the circumcircle is
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