Answer to Question #115619 in Calculus for Rothama

Question

The equation x^2+y^2+z^2+8x−6y+2z+17=0 represents a sphere. The radius of the sphere is,
Select one:
a. √3

b. 9
c. 3
d. 17
e. √17

Answer 1

Consider the equation of circle $x^2+y^2+z^2+8x-6y+2z+17=0$

Complete square for each coordinate points $x,y$ and $z$ as,

$x^2+8x+y^2-6y+z^2+2z+17=0$

$x^2+2(4)x+4^2-4^2+y^2-2(3)y+3^2-3^2+z^2+2(1)z+1^2-1^2+17=0$

$(x+4)^2-16+(y-3)^2-9+(z+1)^2-1+17=0$

$(x+4)^2+(y-3)^2+(z+1)^2-26+17=0$

$(x+4)^2+(y-3)^2+(z+1)^2-9=0$

$(x+4)^2+(y-3)^2+(z+1)^2=9$

$(x+4)^2+(y-3)^2+(z+1)^2=3^2$

Therefore, the radius of the sphere is $3$ .

Hence, option (c) is correct.