Answer
(a) The sphere has symmetry with respect to this line.
(b) The sphere does not have symmetry with respect to this plane.
Work Step by Step
We can write the general equation of a sphere:
$(x-a)^2+(y-b)^2+(z-c)^2 = r^2$
where $(a,b,c)$ is the center of the sphere and $r$ is the radius
The equation of the sphere is: $x^2+y^2+z^2 = 100$
The center of the sphere is $(0,0,0)$
(a) A sphere has symmetry with respect to any line that passes through the sphere's center. Since the line passing through the points $(0,0,0)$ and $(0,5,5\sqrt{5})$ passes through the point $(0,0,0)$, the sphere has symmetry with respect to this line.
(b) A sphere has symmetry with respect to any plane that includes the sphere's center. Since the plane with the equation $y=5$ does not include the point $(0,0,0)$, the sphere does not have symmetry with respect to this plane.
