#### 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.