How do you convert #r^2sin2t=2# into cartesian form?

1 Answer
Shwetank Mauria
Jun 3, 2016

In Cartesian form #r^2sin2t=2# can be written as
#xy=1#, which is the equation of a hyperbola.

Explanation:

The relation between a polar coordinate #(r,t)# and Cartesian coordinates #(x,y)# is given by #x=rcost# and #y=rsint#

Also note that #r^2=x^2+y^2# and #y/x=tantheta#

Hence #r^2sin2t=2# can be written as

#r^2xx2sintcost=2# or #rsintxxrcost=1#

or #xy=1#, which is the equation of a hyperbola.

graph{xy=1 [-10, 10, -5, 5]}

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