Question

How do you convert `r^2= sec2theta` to polar form?

Answer 1

`x^2-y^2=1`

Explanation:

The relation between polar coordinates `(r,theta)` and Cartesian coordinates `(x,y)` is

`x=rcostheta`, `y=rsintheta` i.e. `x^2+y^2=r^2`

Hence `r^2=sec2theta` can be written as

`r^2=1/(cos2theta)=1/(cos^2theta-sin^2theta)`

or `r^2cos^2theta-r^2sin^2theta=1`

or `x^2-y^2=1`
graph{x^2-y^2=1 [-10, 10, -5, 5]}