The equation is (x − 0)² + (y − 0)² + (z − 0)² = (√202)². Then the radius is √202, and the center of the sphere is (0, 0, 0).
It is a locus of a point drawn at an equidistant from the center. The distance from the center to the circumference is called the radius of the circle.
The function r(t) traces a circle is given as
[tex]\rm r(t)=-9i+ (11cos \ t)j+ (11sin \ t)k[/tex]
Let the component along the x-axis, y-axis, and z-axis.
[tex]\rm x = - 9\\\\y = 11 cos \ t\\\\z = 11 sin \ t[/tex]
Now we can simplify it,
[tex]\rm x ^2 + y^2 + z ^2 = 81 + 121 cos ^2t + 121 sin ^2t\\\\x ^2 + y^2 + z ^2 = 81 + 121 (cos ^2t + sin ^2t)\\\\x ^2 + y^2 + z ^2 = 81 + 121 \\\\x ^2 + y^2 + z ^2 = 202[/tex]
We can also write it as
[tex](x-0)^2+(y-0)^2 + (z-0)^2 = (\sqrt{202})^2[/tex]
Now compare with a standard equation, we have
[tex](x-0)^2+(y-0)^2 + (z-0)^2 = (r)^2[/tex]
Thus, the radius is √202, and the center of the sphere is (0, 0, 0)
More about the circle link is given below.
https://brainly.com/question/11833983
