Q 38. - Calculus

Question

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

$r=-3 \sec \theta$

Step-by-Step Solution

Answer

The required equation is $x=-3$.

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 $x=-3$.