Convert the equation from rectangular to polar form and draw its graph? #xy=4#

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Answer 1 · 2017-06-12T17:54:54

#r = 2/sqrt(cos(theta)sin(theta))#

Here is a graph of the converted equation:![Desmos.com]( useruploads.socratic.org )

Here is the graph of #xy=4# (before the conversion)

![Desmos.com]( useruploads.socratic.org )

To convert to polar form, substitute #x = rcos(theta)# and #y = rsin(theta)#:

#rcos(theta)rsin(theta)=4#

Use algebra to write r as a function of #theta#:

#r^2= 4/(cos(theta)sin(theta))#

#r = 2/sqrt(cos(theta)sin(theta))#