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Question
Find the equation of the circle which circumscribes the triangle formed by the lines x + y + 3 = 0, x − y + 1 = 0 and x = 3
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Solution
In \[∆\]
(i) Let AB represent the line x + y + 3 = 0. ...(1)
Let BC represent the line x − y + 1 = 0. ...(2)
Let CA represent the line x = 3. ...(3)
Intersection point of (1) and (3) is \[\left( 3, - 6 \right)\]
Intersection point of (1) and (2) is (−2, −1).
Intersection point of (2) and (3) is (3, 4).
Therefore, the coordinates of A, B and C are \[\left( 3, - 6 \right)\], (−2, −1) and (3, 4), respectively.
Let the equation of the circumcircle be \[x^2 + y^2 + 2gx + 2fy + c = 0\]
It passes through A, B and C.
∴ \[45 + 6g - 12f + c = 0\]
Hence, the required equation of the circumcircle is
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