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If the lines x+y=6 and x+2y=4 are diamet...

If the lines `x+y=6 and x+2y=4` are diameters of the circle which passes through the point (2, 6), then find its equation.

Text Solution

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Here center will be the point of intersection of the diameter, i.e., `C (8,-2)`.
Also, the circle passes through the point P(2,6). Then radius is `CP=10`.
Hence, the required equation is
`(x-8)^(2)+(y+2)^(2)=10^(2)`
or `x^(2)+y^(2)-16x+4y-32=0`
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