Question

In Exercises 32–47 convert the equations given in polar coordinates to rectangular coordinates.

$r=-3\sec \theta$

Short answer

The required equation is$x=-3$.

Step-by-step solution

Step 1. Given information.

The given equation in polar coordinates is:

$r=-3\sec \theta$

Step 2. Find the equation in rectangular coordinates.

$$\begin{gathered} r=-3\sec \theta \\ r=-3·\frac{1}{\cos \theta } \\ r\cos \theta =-3 \\ x=-3\left[\mathrm{Since}r\cos \theta =x\right] \end{gathered}$$

Therefore, the equation in rectangular coordinates is$x=-3$.