# Convert y=3x+4 to Polar form

1. Sep 12, 2007

### GloryUs

1. The problem statement, all variables and given/known data
Write equation in polar form. y=3x+4

2. Relevant equations
x^2 + y^2 = r^2
x = rcos(theta)
y = rsin(theta)
tan(theta) = y/x

3. The attempt at a solution

Square both sides...
y^2 = 9x^2 + 24x + 16

r^2 - x^2 = 9x^2 +24x +16

r^2 = 10x^2 + 24x + 16

And that's where I got stuck...

2. Sep 12, 2007

### learningphysics

Don't do it like that. Substitute the polar form of x and y into your equation... and you'll be done.

3. Sep 12, 2007

### HallsofIvy

Staff Emeritus
Replace EVERY x with $r cos(\thet$ and EVERY y with $r sin(\theta)$

4. Sep 12, 2007

### JonF

What is your goal in converting from Cartesian to polar coordinates? You want to get a function that is:
r = a bunch of theta junk

So how do we turn y=3x+4 into an equation of nothing but r’s and theta’s? We use the two substations you have, then we get r all by it self on one side.