The part of the sphere x2 + y2 + z2 = 36 that lies above the cone z = x2 + y2 . (Enter your answer as a comma-separated list of equations. Let x, y, and z be in terms of u and/or v.)

Step-by-step explanation:

Given that:

The equation of the sphere is = x² + y² + z² = 36;  &

The cone z =

The first process is to evaluate the intersection of these curves.

i.e.

2(x² + y²) = 36

Dividing both sides 2, we get;

x² + y² = 36

Suppose the parameterization of x=u, y=v;

Thus, the sphere result to:

x² + y² + z² = 36

Making z² the subject of the formula:

z² = 36 - x² - y²

Now, to evaluate z in terms of  u and v, we have:

Thus, the expected parametric representation for the surface is: