The intercept on the line `y = x` by the circel `x^2 + y^2 - 2x = 0` is AB. Equation of the circle with AB as a diameter is

Answer

`x^(2)+y^(2)-x-y=0`

Explanation

Equation of any circle passing through the point of lt brgt intersection of `x^(2)+y^(2)-2x=0 and y=x`is
`(x^(2)+y^(2)-2x)+lambda(y-x)=0`
`rArr x^(2)+y^(2)-(2+lambda)x+lambday=0`
Its centre is `((2+lambda)/(2),(-lambda)/(2))`.
`rArr` For AB to be the diameter of the required circle the centre must be on AB, i.e.
`2+lambda=-lambda`
`rArr lambda = -1 " "[therefore y = x]`
therefore, equation of the required circle is
`x^(2)+y^(2)=(2-1)x-1*y=0`
`rArr x^(2)+y^(2)-x-y=0`