How do you convert the following to polar coordinates 2xy=1?

1 Answer
Jan 8, 2016

I think the question is convert to a polar equation. You use the rectangular conversion equations.

Explanation:

Based on the circular definitions of the trigonometric functions of sine and cosine you have the following:
sin theta = y/r and cos theta=x/r.

therefore:

y=rsintheta using algebra and
x=rcostheta using algebra.
These are the conversion from rectangular (x,y) to polar (r,theta)

So in the equation 2xy=1 you simply substitute.

2*rcostheta*rsintheta=1
2costheta*sintheta*r^2=1
sin(2theta)*r^2=1

so your polar equation is:

r^2=csc^2(2theta)