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

Options

A. `x^(2)+y^(2)+x+y=0`
B. `x^(2)+y^(2)-x-y=0`
C. `x^(2)+y^(2)-3x+y=0`
D. `x^(2)+y^(2)+3x-y=0`

Answer

B

Explanation

We have equation of line y=x and equation of circle `x^(2)+y^(2)-2x=0`

Now, intersecting points of given line and circle,
`x^(2)+x^(2)-2x=0`
`implies2x^(2)-2x=0`
`implies2x(x-1)=0`
`impliesx=0,1`
when x=0 then y=0 and when x=1 then y=1
`therefore`Coordinates of end points of diameter AB are (0,0) and (1,1). `therefore` Required equation of circle with diameter AB.
`(x-0)(x-1)+(y-0)(y-1)=0`
`impliesx^(2)-2+y^(2)-y=0`
`impliesx^(2)+y^(2)-x-y=0`