Question

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

• A. $x^2+y^2-x-y=0$
• B. $x^2+y^2-x+y=0$
• C. $x^2+y^2+x+y=0$
• D. $x^2+y^2+x-y=0$

Answer 1

The correct option is A $x^2+y^2-x-y=0$

The equation of the line is
y = x ......(i)
and the equation of the circle is
$x^2+y^2-2x=0$ .......(ii)
On solving (i) and (ii), we get
$x^2+x^2-2x=0\Rightarrow 2x^2-2x=0\Rightarrow 2x(x-1)=0\Rightarrow x=0,x=1Whenx=0,y=0.Whenx=1,y=1.\therefore$
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
$(x-x_1)(x-x_2)+(y-y_1)(y-y_2)=0\Rightarrow (x-0)(x-1)+(y-0)(y-1)=0\Rightarrow x(x-1)+y(y-1)=0\Rightarrow x^2+y^2-x-y=0$