1.

Find the centre and radius of the circle x2 + y2 - 2x - 2y = 0​

Answer»

Given Equation

x^2+y^2-2x-2y

=(x^2-2x+1)+(y^2-2y+1)-2

=(x-1)^2+(y-1)^2-2

\therefore (x-1)^2+(y-1)^2=2

Application of Distance Formula

\sqrt{(x-1)^2+(y-1)^2} =\sqrt{2}

→ The distance from (x,y) and (1,1) is \sqrt{2}. [Distance Formula]

Thus, this equation FORMS a CIRCLE with center (1,1) and RADIUS of \sqrt{2}.


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