Find the largest real number x for which there exists a real number y such that x^2 + y^2 = 2x + 2y.

Rollingblade Dec 1, 2018

#1**+2 **

Circle's general form is \(ax^2 + by^2 + cx + dy + e = 0.\)

We want to rewrite \(x^2 + y^2 = 2x + 2y\) to its standard form.

\(x^2 + y^2 = 2x + 2y\\ x^2-2x+y^2-2y=0\\ x^2-2x+1+y^2-2y+1=2\\ (x-1)^2+(y-1)^2=2\)

The circle has a center of \((1,1)\) and a radius of \(\sqrt2. \)

Largest *x *value on the circle graph is farthest right, \(\boxed{1+\sqrt2}\)

If there is any part you don't understand, please message me

GYanggg Dec 1, 2018

#1**+2 **

Best Answer

Circle's general form is \(ax^2 + by^2 + cx + dy + e = 0.\)

We want to rewrite \(x^2 + y^2 = 2x + 2y\) to its standard form.

\(x^2 + y^2 = 2x + 2y\\ x^2-2x+y^2-2y=0\\ x^2-2x+1+y^2-2y+1=2\\ (x-1)^2+(y-1)^2=2\)

The circle has a center of \((1,1)\) and a radius of \(\sqrt2. \)

Largest *x *value on the circle graph is farthest right, \(\boxed{1+\sqrt2}\)

If there is any part you don't understand, please message me

GYanggg Dec 1, 2018