Find center and radii of a circule

[lucky strike]

Homework Statement

2x^2+2y^2+2z^2+x+y+Z=9
find center and radii of the sphere

Homework Equations

moving like terms yeilds

2x^2 + x + _ + 2y^2 + y + _ + 2z^2 + z + _ = 9

The Attempt at a Solution

divide out the 2 yeilds

2[ x^2 + 1/2x + _ + y^2 + 1/2y + _ + z^2 + 1/2z + _ ] = 9/2

complete the square

1/2 / 2 = (1/4)^2 = 1/16

adding term in

x^2 + 1/2x + 1/16 + y^2 + 1/2y + 1/16 + z^2 + 1/2z + 1/16 = 9/2 + 3/16

solving right side

9/2 + 3/16 = 72/16 + 3/16 = 75/16

factoring left side

(x + 1/4)^2 + (y + 1/4)^2 + (z + 1/4)^2

solving

center = C{-1/4,-1/4,-1/4}
radii = sqrt of 75/16 = (5 sqrt 3) / 4

whoot!

 

[HallsofIvy]

Homework Statement

2x^2+2y^2+2z^2+x+y+Z=9
find center and radii of the sphere

Homework Equations

moving like terms yeilds

2x^2 + x + _ + 2y^2 + y + _ + 2z^2 + z + _ = 9

The Attempt at a Solution

divide out the 2 yeilds

2[ x^2 + 1/2x + _ + y^2 + 1/2y + _ + z^2 + 1/2z + _ ] = 9/2

Either drop the "2" at the start or the "2" in "9/2"- you can't have them both!

complete the square

1/2 / 2 = (1/4)^2 = 1/16

adding term in

x^2 + 1/2x + 1/16 + y^2 + 1/2y + 1/16 + z^2 + 1/2z + 1/16 = 9/2 + 3/16

Okay, now that leading "2" is gone.

solving right side

9/2 + 3/16 = 72/16 + 3/16 = 75/16

factoring left side

(x + 1/4)^2 + (y + 1/4)^2 + (z + 1/4)^2

solving

center = C{-1/4,-1/4,-1/4}
radii = sqrt of 75/16 = (5 sqrt 3) / 4

whoot!

Looks good to me!

 

[Architeuthis Dux]

Great job on finding the center and radii of the sphere! Your method of completing the square was a great approach to solving this problem. Keep up the good work!