# Homework Help: Translate the rectangular equation to spherical

1. Sep 9, 2012

### whynot314

Translate the rectangular equation to spherical and cylindrical equations.

http://www.texify.com/img/%5CLARGE%5C%21x%5E2%2By%5E2%2B2y-3x%2Bz%5E2%3D25.gif [Broken]

Last edited by a moderator: May 6, 2017
2. Sep 9, 2012

### SammyS

Staff Emeritus
Hello whynot314. Welcome to PF!

What have you tried?

Where are you stuck?

We can't help you until you show us what you tried. It in the rules .

Last edited by a moderator: May 6, 2017
3. Sep 10, 2012

### whynot314

I first transformed x^2+y^2+z^2 into ρ^2

ρ^2+2ρsinϕsinθ-3ρsinϕcosθ=25

then factored out a ρ

ρ(ρ+2sinϕsinθ-3sinϕcosθ)=25

I want to solve for ρ,

I am confused as to, weather or not subtract 25 and set it equal to zero or keep it like this and have two equations where

ρ=25

and

ρ=25-2sinϕsinθ+3sinϕcosθ

4. Sep 10, 2012

### HallsofIvy

Then what you need is a good class in arithmetic! If ab= c it does NOT follow that "a= c or b= c!!

If that isn't enough, if xy= 10, it does NOT follow that either x= 10 (and y= 1) or y= 10 (and x= 1). There are an infinite number of soutions to xy= 10.

5. Sep 10, 2012

### SammyS

Staff Emeritus
How can you say ρ = 25 ?

ρ2 + 2ρsinϕsinθ-3ρsinϕcosθ = 25 is quadratic in ρ .

Complete the square or use the quadratic formula to solve for ρ.

For either, you may want to rewrite your equation as:
ρ2 + 2ρsinϕ(sinθ-cosθ) = 25​
$\sin^2\phi\left(\sin\theta-\cos\theta\right)^2$​