Question: Solve question 7 please. 7. If the curve y = g(z) is revolved about the z-axis, then the resulting sur- face of revolution has x2

Solve question 7 please.

7. If the curve y = g(z) is revolved about the z-axis, then the resulting sur- face of revolution has x2 + 12 = g(z) as its equation. A convenient para- metric representation of this surface is given by x = g(z) cos 0, y = 8(z) sin 0, z = z, where 0 is the polar angle in the xy-plane. Show that a geodesic 0 = 0(z) on this surface has 0 = C1 (1+ [8'(z) 12 8 (z) V8(2)2- c dz + C2 as its equation

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