Solve: $x^{2} + y^{2} - 4 x - 4 y + 8 = 0$ .

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Solution

Given,
$x^{2} + y^{2} - 4 x - 4 y + 8 = 0$
or, $x^{2} - 4 x + 4 + y^{2} - 4 y + 4 = 0$
or, $(x - 2)^{2} + (y - 2)^{2} = 0$
This gives $x - 2 = 0, y - 2 = 0 \Rightarrow x = 2, y = 2.$

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Solve: x2+y2−4x−4y+8=0.

Given,x2+y2−4x−4y+8=0or, x2−4x+4+y2−4y+4=0or, (x−2)2+(y−2)2=0This gives x−2=0,y−2=0⇒x=2,y=2.

Solve: $x^{2} + y^{2} - 4 x - 4 y + 8 = 0$ .

Given,
$x^{2} + y^{2} - 4 x - 4 y + 8 = 0$
or, $x^{2} - 4 x + 4 + y^{2} - 4 y + 4 = 0$
or, $(x - 2)^{2} + (y - 2)^{2} = 0$
This gives $x - 2 = 0, y - 2 = 0 \Rightarrow x = 2, y = 2.$