Asked by Anonymous
Show that the equation represent a sphere, and find it center and radius 3x^2 +3y^2 + 3z^2=10+6y+12z
Answers
Answered by
oobleck
Remember what you did with circles in Algebra II -- complete the squares.
3x^2 +3y^2 + 3z^2=10+6y+12z
3x^2 + 3y^2-6y + 3z^2-12z = 10
3x^2 + 3(y^2-2y+1) + 3(z^2-4z+4) = 10 + 3*1 + 3*4
and so on to the end.
3x^2 +3y^2 + 3z^2=10+6y+12z
3x^2 + 3y^2-6y + 3z^2-12z = 10
3x^2 + 3(y^2-2y+1) + 3(z^2-4z+4) = 10 + 3*1 + 3*4
and so on to the end.