Find the equation of the circle which passes through the points (20, 3), (19, 8) and (2, –9). Find its centre and radius.
Find the equation of the circle which passes through the points (20, 3), (19, 8) and (2, –9). Find its centre and radius.
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By substitution of coordinates in the general equation of the circle given by x2 + y2 + 2gx + 2fy + c = 0,
we have
40g + 6f + c = – 409
38g + 16 f + c = – 425
4g – 18 f + c = – 85
From these three equations, we get
g = – 7, f = – 3 and c = –111
Hence, the equation of the circle is
x2 + y2 – 14x – 6y – 111 = 0
or (x – 7)2 + (y – 3)2 = 132
Therefore, the centre of the circle is (7, 3) and radius is 13.
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