contestada

Find a parametrization, using cos(t) and sin(t), of the following curve: The intersection of the plane y= 5 with the sphere

x^2+y^2+z^2=125

Respuesta :

The parametrization shown below,

            [tex]x(t),y(t),z(t)=10cost,5,10sint[/tex]

Given equation of sphere,

                 [tex]x^{2} +y^{2} +z^{2} =125[/tex]

Substitute y = 5 in above relation.

         [tex]x^{2} +z^{2}=125-25=100\\ \\x^{2} +z^{2}=10^{2}[/tex]

For parametrization,

Substitute [tex]x=rcos(t),z=rsin(t)[/tex] and [tex]r=10[/tex]

So that,  [tex]x(t),y(t),z(t)=10cost,5,10sint[/tex]

Learn more:

https://brainly.com/question/23070611

Otras preguntas