Answer:
Step-by-step explanation:
Given that:
The equation of the sphere is = x² + y² + z² = 36; &
The cone z = [tex]\sqrt{x^2+y^2}[/tex]
The first process is to evaluate the intersection of these curves.
i.e.
[tex]x^2 + y^2 + ( \sqrt{x^2 +y^2})^2=36[/tex]
[tex]x^2 + y^2 + ( {x^2 +y^2})=36[/tex]
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
[tex]z = \sqrt{36-x^2-y^2}[/tex]
Now, to evaluate z in terms of u and v, we have:
[tex]z = \sqrt{36-u^2-v^2}[/tex]
Thus, the expected parametric representation for the surface is:
[tex]r(u,v) =\bigg \langle u,v, \ \sqrt{36-u^2-v^2} \bigg \rangle, where \ \ u^2 +v^2 = 18[/tex]
