Find the Radius and Center of a Sphere, Quadric Surfaces

[Unicow]

Homework Statement

[/B]
Find the radius and center of sphere
ρ = 28 cos ϕ.

Homework Equations

Relevant equations would be the spherical and rectangular coordinate equations.

The Attempt at a Solution

I started off by multiplying both sides of the equation by ρ to get

ρ^2 = 28 ρ cosϕ

Then this would allow me to get to the equation of a sphere which is

x^2 + y^2 + z^2 = 28z

I don't really know where to go from here. Could someone point me in the right direction? I can't really seem to find how to get rid of the z. I know the a^2 under x,y,z will give me the radius if I just take a.

 

[Mark44]

Homework Statement

[/B]
Find the radius and center of sphere
ρ = 28 cos ϕ.

Homework Equations

Relevant equations would be the spherical and rectangular coordinate equations.

The Attempt at a Solution

I started off by multiplying both sides of the equation by ρ to get

ρ^2 = 28 ρ cosϕ

Then this would allow me to get to the equation of a sphere which is

x^2 + y^2 + z^2 = 28z

I don't really know where to go from here. Could someone point me in the right direction? I can't really seem to find how to get rid of the z. I know the a^2 under x,y,z will give me the radius if I just take a.

From your last equation, $x^2 + y^2 + z^2 - 28z = 0$
Complete the square in the z terms. You'll have a sphere whose center is at (0, 0, ?).

 

[Unicow]

From your last equation, $x^2 + y^2 + z^2 - 28z = 0$
Complete the square in the z terms. You'll have a sphere whose center is at (0, 0, ?).

You are an absolute life saver haha. Such a simple solution, I really need to learn to think outside the box... .