+239 Find the largest real number x for which there exists a real number y such that x^2 + y^2 = 2x + 2y.
+983 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
+983 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
