Rewriting an Equation with Polar Substitutions

[Centurion1]

Homework Statement

Rewrite the given equation using the substitutions x=rcos@ and y=rsin@

THETA EQUAL @
x² + y² +5x =0

Homework Equations

The Attempt at a Solution

you plug in the subsititutions first. Then you factor it?

 

[CompuChip]

Well, just plug it in?

 

[Дьявол]

Plug them in, then factor out r², and after that, factor r, and you will come up with 2 solutions for r.

Regards.

 

[statdad]

I see nothing in the OPs first message that states anything more than transforming the original equation needs to be done. Make the given substitution: you will be able to make some simplification because of the squared terms, even factor, but unless there are instructions that weren't posted, I wouldn't bother factoring (were you asked to do something after you transform the equation?)

 

[Centurion1]

I ended up just factoring it. It was far easier than i thought it would be. I just wanted to make sure of how i was doing it.

 

[Mentallic]

Factoring would be best here because it helps you to notice that the equation can be simplified because of the $$sin^2\theta+cos^2\theta=1$$

 

[CompuChip]

Well, if you got $r^2 + 5 r \cos\theta$ you did it correctly :)

When you get more "into" polar coordinates, you will start to notice immediately that x² + y² is actually precisely r², where r is defined as the distance $\sqrt{x^2 + y^2}$ from the point (x, y) to the origin. But if you don't see that right away, you can just plug in the formula and use the identity posted by Mentallic (which you should remember for life anyway).