Viviani 's Curve C is the intersection of the surfaces x2 y2 z2, y z2 (a) Parametrize each of the two parts of C corresponding to x yen 0 and x curren 0, taking t z as parameter (b) Describe the projection of C onto the xy plane (c) Show that C lies on the sphere of radius 1 with center (0, 1, 0) T...

a We must solve for y and x in terms of z which is a parameterWe get Here the from x z 2 z 4 represe ...

Viviani's Curve C is the intersection of the surfaces x2 + y2 = z2, y = z2

Question:

Viviani's Curve C is the intersection of the surfaces
x2 + y2 = z2, y = z2
(a) Parametrize each of the two parts of C corresponding to x ‰¥ 0 and x ‰¤ 0, taking t = z as parameter.
(b) Describe the projection of C onto the xy-plane.
(c) Show that C lies on the sphere of radius 1 with center (0, 1, 0). This curve looks like a figure eight lying on a sphere