Question

$e=1$; directrix is parallel to the polar axis $2$units below the

pole.

Short answer

The polar equation is

$r=\frac{2}{1-\sin \left(\theta \right)}$

Step-by-step solution

Step 1. Given information 

$e=1$; directrix is parallel to the polar axis $2$units below the

pole.

Step 2. Identify e and p

It is given that

$e=1$

And directrix is parallel to the polar axis $2$units below the

pole

So,$p=2$

Step 3. Set up the polar equation

It is given that

focus is at the pole.

The directrix is parallel to the polar axis $2$units below the

pole.

So, we can apply standard polar equation formula

$r=\frac{ep}{1-e\sin \left(\theta \right)}$

Plug values $e=1,p=2$

$$\begin{gathered} r=\frac{1\times 2}{1-1\sin \left(\theta \right)} \\ r=\frac{2}{1-\sin \left(\theta \right)} \end{gathered}$$