SOLUTION: Convert the general form of the circle given into standard form. 2x^2 + 2y^2 - 20x - 8y + 50 = 0

Algebra.Com
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:
-----
x^2-10x+a + y^2-4y+b = -25+a+b
-----
x^2-10x+25 + y^2-4y+4 = -25+25+4
----
(x-5)^2 + (y-2)^2 = 4
========
Cheers,
Stan H.
============

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






RELATED QUESTIONS

The general form of an equation of a circle is given. Convert to the standard form. (answered by josgarithmetic,ikleyn,greenestamps,math_tutor2020,MathTherapy)
Write the equation of the given parabola in general form: -14x + 2y^2 -8y... (answered by stanbon)
Convert the general equation to standard form of a parabola... (answered by josgarithmetic)
write the equation of the given circles in standard form: 1) x^2+y^2-6x+8y+9=0 2)... (answered by venugopalramana)
The following equation is the general form of the circle 2x^2 - 5x + 2y^2 - 7y = 0.... (answered by Theo)
How do you convert x^2-2y^2-4y-6=0 into the standard form of a hyperbola? (answered by josgarithmetic)
Change the circle equation from standard form into general form... (answered by Fombitz)
How do you convert the equation y=3x+2 into general form... (answered by mananth)
Convert the equation to standard form by completing the square... (answered by MathLover1)