Homework Sourseshow that the equation 4x2 4y2 4z2 8x 24y 4z 29 represe
show that the equation 4x^2 + 4y^2 + 4z^2 + 8x - 24y 4z = -29 represent a sphere in 3-space. Find its center and radius.
Solution
As sign before 4z is not given so any of the soln is possible ; check carefully 4x^2 + 8x + 4y^2 + 4z^2 - 24y- 4z = -29 4(x^2 + 2x +1) + 4 ( y^2 - 6y +9)+ 4(z^2-z+0.25) = -29 +4+36+1 =12 (x+1)^2 + (y-3)^2 + (z-0.5)^2 = 3 centre (-1,3,0.5); radius = sqrt(3) OR 4x^2 + 8x + 4y^2 + 4z^2 - 24y + 4z = -29 4(x^2 + 2x +1) + 4 ( y^2 - 6y +9)+ 4(z^2+z+0.25) = -29 +4+36+1 =12 (x+1)^2 + (y-3)^2 + (z+0.5)^2 = 3 centre (-1,3,-0.5); radius = sqrt(3)
