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ight) = x^2 + y^2 + z^2.
Multiply through:
9c^2 - rac{9c^2 z^2}{x^2 + y^2 + z^2} = x^2 + y^2 + z^2.
Multiply both sides by \(x^2 + y^2 + z^2\):
9c^2(x^2 + y^2 + z^2) - 9c^2 z^2 = (x^2 + y^2 + z^2)^2.
9c^2(x^2 + y^2) = (x^2 + y^2 + z^2)^2.
This is the equation of a **torus** centered along the \(z\)-axis with major radius \(3c\) and minor radius \(3c\), but more precisely, from the original form \(
ho = 3c \sin(\phi)\), this describes a **sphere** of radius \( rac{3c}{2}\) centered at \((0, 0, rac{3c}{2})\) in Cartesian coordinates. To verify, note that:
ho = 2a \sin\phi \Rightarrow ext{sphere of radius } a ext{ centered at } (0,0,a).
Here, \(2a = 3c \Rightarrow a = rac{3c}{2}\), so the shape is a sphere of radius \( rac{3c}{2}\) centered at \((0, 0, rac{3c}{2})\).