Question

How do you convert `r=4sec(theta)(1+ tan(theta))` into cartesian form?

Answer 1

`1/4=1/x+1/y`

Explanation:

Polar coordinates `(r,theta)` and Cartesian coordinates `(x,y)` are related as

`x=rcostheta` and `y=rsintheta`, i.e. `tantheta=y/x`

Hence, `r=4sectheta(1+tantheta)` can be written as

`rcostheta=4(1+tantheta)`

or `y=4(1+y/x)`

or `xy=4x+4y`

or `(xy)/(4xy)=(4x)/(4xy)+(4y)/(4xy)`

or `1/4=1/y+1/x` or `1/4=1/x+1/y`