Question

How do you find the rectangular equation for `r=sectheta`?

Answer 1

see below

Explanation:

The relation between rectangular and polar coordinates is
`x=rcostheta ,y=rsin theta` ---(1)
Squaring and adding, we get `r^2=x^2+y^2`
From (1), we have `y/x=tan theta`
the given equation is `r=sec theta`
Squaring, we get `r^2=sec^2 theta` or `r^2=1+tan^2 theta`
The required rectangular equation is
`x^2+y^2=1+y^2/x^2` or
`x^4+x^2y^2-x^2-y^2=0`