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

May 25, 2018

see below

#### Explanation:

The relation between rectangular and polar coordinates is
$x = r \cos \theta , y = r \sin \theta$ ---(1)
Squaring and adding, we get ${r}^{2} = {x}^{2} + {y}^{2}$
From (1), we have $\frac{y}{x} = \tan \theta$
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
${x}^{4} + {x}^{2} {y}^{2} - {x}^{2} - {y}^{2} = 0$