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Question
Find the equation of the circle circumscribing the rectangle whose sides are x − 3y = 4, 3x + y = 22, x − 3y = 14 and 3x + y = 62.
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Solution
Given:
Sides of the rectangle:
x − 3y = 4 ...(1)
3x + y = 22 ...(2)
x − 3y = 14 ...(3)
And, 3x + y = 62 ...(4)
The intersection of (1) and (2) is (7, 1).
The intersection of (2) and (3) is (8, −2).
The intersection of (3) and (4) is (20, 2).
The intersection of (1) and (4) is (19, 5).
Hence, the vertices of the rectangle are (7, −1), (8, −2), (20, 2) and (19, 5).
The vertices of the diagonals are (7, −1), (20, 2) and (19, 5), (8, −2).
Thus, the required equation of the circle is
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