# Thread: polar to rect form conversion

1. ## polar to rect form conversion

Hi. I'm working on a practice problem which is stumping me. Even after looking up the answer in the back of the book, I still don't understand how it was arrived at.

The question involves taking polar equation

r = 2(h*cos(t)+k*sin(t))

And coverting it to rectangular form, and verifying that it is the equation of a circle.

I keep playing around with the coord conversion equations and trig identities, but I can't seem to get it worked out. Help!

2. ## Re: polar to rect form conversion

Originally Posted by infraRed
Hi. I'm working on a practice problem which is stumping me. Even after looking up the answer in the back of the book, I still don't understand how it was arrived at.

The question involves taking polar equation

r = 2(h*cos(t)+k*sin(t))

And coverting it to rectangular form, and verifying that it is the equation of a circle.

I keep playing around with the coord conversion equations and trig identities, but I can't seem to get it worked out. Help!
$r = \sqrt{x^2 + y^2}$, $cos(t) = \frac{x}{\sqrt{x^2 + y^2}}$, and $sin(t) = \frac{y}{\sqrt{x^2 + y^2}}$

Hint: Plug these into your equation and multiply both sides by $\sqrt{x^2 + y^2}$.

-Dan

3. ## Re: polar to rect form conversion

Originally Posted by infraRed
Hi. I'm working on a practice problem which is stumping me. Even after looking up the answer in the back of the book, I still don't understand how it was arrived at.

The question involves taking polar equation

r = 2(h*cos(t)+k*sin(t))

And coverting it to rectangular form, and verifying that it is the equation of a circle.

I keep playing around with the coord conversion equations and trig identities, but I can't seem to get it worked out. Help!
if (h $\neq$ k) then it's not a circle, it's an ellipse.