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Question 429396: Convert the general form of the circle given into standard form.
2x^2 + 2y^2 - 20x - 8y + 50 = 0
Found 2 solutions by stanbon, Edwin McCravy:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Convert the general form of the circle given into standard form.
2x^2 + 2y^2 − 20x − 8y + 50 = 0
Divide thru by 2:
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x^2-10x+a + y^2-4y+b = -25+a+b
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x^2-10x+25 + y^2-4y+4 = -25+25+4
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(x-5)^2 + (y-2)^2 = 4
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Cheers,
Stan H.
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Answer by Edwin McCravy(20060)  (Show Source):
You can put this solution on YOUR website!
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 + 25 + 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 + 25 + y² - 4y + 4 = -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
Edwin
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