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

Question

30742 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-01-08T23:53:49

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

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)#