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

Dec 1, 2018

#1
+974
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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 value on the circle graph is farthest right, $$\boxed{1+\sqrt2}$$

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

Dec 1, 2018

#1
+974
+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 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