Question 429396
<pre><font face = "consolas" color = "indigo" size = 4><b>
2x² + 2y² - 20x - 8y + 50 = 0

Divide through by 2

x² + y² - 10x - 4y + 25 = 0

Swap the 2nd and 3rd terms to get the terms in x together
and the terms in y togethsr

x² - 10x + y² - 4y + 25 = 0

Get the 25 off the left side by subtracting 25 from both sides:

x² - 10x + y² - 4y = -25 

Skip a space after the x terms and after the y terms:

x² - 10x + __ + y² - 4y + __ = -25

Complete the square on the x terms:

1.  To the side, nultiply the coefficient of x, which is -10,
    by 1/2, getting -5
2.  Then square the -5 you got in step 1, getting +25  
3.  Put 25 in the first blank and add 25 to the right side 

x² - 10x + <u>25</u> + y² - 4y + __ = -25 + 25

Complete the square on the y terms:

1.  To the side, nultiply the coefficient of y, which is -4,
    by 1/2, getting -2
2.  Then square the -2 you got in step 1, getting +4  
3.  Put 4 in the second blank and add 4 to the right side 

x² - 10x + <u>25</u> + y² - 4y + <u>4 </u> = -25 + 25 + 4

Factor the first three terms on the left
Factor the last three terms on the left
Combine the terms on the right

(x - 5)(x - 5) + (y - 4)(y - 4) = 4

Write as squares of binomials:

            (x - 5)² + (y - 4)² = 4

Compare to

            (x - h)² + (y - k)² = r² 

The center is (h,k) = (5,4)

The radius is four from r² = 4 which gives r = 2

The graph is

{{{drawing(400,400,-2,8,-2,8,
circle(5,4,.05),
graph(400,400,-2,8,-2,8), circle(5,4,2))}}}

Edwin</pre>