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Question

The intercept on the line y = x by the circle x2+y22x=0 is AB. The equation of the circle on AB as a diameter is 
  1. x2+y2+x+y=0
  2. x2+y2+xy=0
  3. x2+y2xy=0
  4. x2+y2x+y=0


Solution

The correct option is C x2+y2xy=0
The equation of the line is 
y = x                          ......(i)
and the equation of the circle is 
x2+y22x=0        .......(ii)
On solving (i) and (ii), we get
x2+x22x=02x22x=02x(x1)=0x=0, x=1When x=0, y=0.When x=1, y=1.
the coordinates of A are (0, 0) and the coordintes of B are (1, 1).
Therefore, the equation of the circle (with AB as a diameter) is
(xx1)(xx2)+(yy1)(yy2)=0(x0)(x1)+(y0)(y1)=0x(x1)+y(y1)=0x2+y2xy=0  

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