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# Find the equation of the circle with centre (1,1) and radius $\sqrt 2$

$\begin {array} {1 1} (A)\;x^2+y^2+2x+2y=0 & \quad (B)\;x^2+y^2-2x-2y=0 \\ (C)\;x^2+y^2-2x+2y=0 & \quad (D)\;x^2+y^2+2x-2y=0 \end {array}$

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• Equation of a circle with centre (h, k) and radius r is given as : $(x-h)^2+(y-k)^2=r^2$
The coordinates of the centre are (1,1) and radius is $\sqrt 2$
$\therefore$ Equation of the circle is
$(x-1)^2+(y-1)^2=( \sqrt 2 )^2$
On expanding we get,
$x^2-2x+1+y^2-2y+1=2$
(i.e) $x^2+y^2-2x-2y=0$
is the required equation of the circle.
answered Jul 11, 2014