Question

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

Answer 1

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]}