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

1 Answer
May 25, 2018

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