Show that the coordinates (x(t), y(t), z(t)) on the curve satisfy the equation of a sphere.
Hey, a pretty basic one here:
Show that the curve given by r = a*cos(t)sin(t)i +a*sin^2(t)j + a*cos(t)k (0<t<pi/2)
lies on a sphere with center at the origin. I have to admit that short of simple plotting I'm rather uncertain at how to tackle this. A hint or two would be great!
You titled this "show that a certain parameterization is a circle". Of course, there are many "non-circle" curves that lie on a sphere. But once you have identified the center of the sphere, you can use that and two points on the curve to determine a plane and then show that the curve also lies on that plane (satisfies the equation of the plane).