# rectangular to polar equation

• Apr 6th 2009, 04:07 PM
ss103
rectangular to polar equation
convert the rectangular to a polar equation:

-8x-3y+5=0

i know that x= r cos theta, as well as other identities

convert the polar to a rectangular equation:
r= 2/ (4-5 cos theta)

i don't even know where to begin here!

thanks
• Apr 6th 2009, 04:14 PM
mr fantastic
Quote:

Originally Posted by ss103
convert the rectangular to a polar equation:

-8x-3y+5=0

i know that x= r cos theta, as well as other identities

Mr F says: Then substitute them into the equation and solve for r.

convert the polar to a rectangular equation:
r= 2/ (4-5 cos theta)

i don't even know where to begin here!

thanks

$\displaystyle r (4 - 5 \cos \theta) = 2 \Rightarrow 4r - 5 r \cos \theta = 2 \Rightarrow 4r - 5x = 2 \Rightarrow 4r = 5x + 2$.

Now square both sides and substitute $\displaystyle x^2 + y^2 = r^2$. Re-arrange into a standard form (looks like it might be a hyperbola).
• Apr 6th 2009, 04:18 PM
ss103
thanks!

but for the first one, i tried to solve it but i dont know how:

-8r cos theta - 3r sin theta +5 =0
where do i go now? do i square it?
• Apr 6th 2009, 04:30 PM
mr fantastic
Quote:

Originally Posted by ss103
thanks!

but for the first one, i tried to solve it but i dont know how:

-8r cos theta - 3r sin theta +5 =0
where do i go now? do i square it?

=> 8r cos theta + 3r sin theta = 5

=> r (8 cos theta + 3 sin theta) = 5

etc.