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

1 Answer
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]}