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Question

Find the equation of the circle which passes through the points (3, 7), (5, 5) and has its centre on the line x - 4y = 1.

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Solution

The circle passes through P and Q and the centre lies on
x4y=1 (i)
The general equation of circle is
x2+y2+2gx+2fy+c=0 (ii)
\because P and Q lies on (ii),
so, 9+49+6g+14f+c=0 (iii)
25+25+lOg+10f+c=0 (iv)
Also, centre (-g, -f) lies on (i)
g+4f=1 (v)
Solving (iii) (iv) and (v), we get
g = 3, f = 1 and c = -90
from (ii)
The equation of circle is
x2+y2+6x+2y90=0


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