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Question

Find the equation of the circle circumscribing the rectangle whose sides are
x3y=4,3x+y=22,x3y=14 and 3x+y=62.

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Solution

The given equation are
x3y=4 (i)3x+y=22 (ii)x3y=14 (iii)3x+y=62 (iv)
Let A, B, C and D are the points of intersection of die lines (i) and (ii), (ii) and (iii), (iii) and (iv), (iv) and (i)
A=(7,1),B=(8,2),C=(20,2) and D=(19,5)
AC will be the diameter of the circle
So,
the equation of circle is
(x7)(x20)+(y1)(y2)=0

x2+y227x3y+142=0


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