Answer:
x = ±8
Step-by-step explanation:
A conic section with a focus at the origin, a directrix of x = ±p where p is a positive real number and positive eccentricity (e) has a polar equation:
[tex]r=\frac{ep}{1 \pm e*cos\theta}\\ \\[/tex]
From the question, the polar equation of the circle is:
[tex]r=\frac{8}{4+cos\theta}[/tex]
We have to make the equation to be in the form of [tex]r=\frac{ep}{1 \pm e*cos\theta}\\ \\[/tex]. Therefore:
[tex]r=\frac{8}{4+cos\theta}\\\\Multiply \ through\ numerator\ and\ denminator\ by\ \frac{1}{4}\\\\ r=\frac{8*\frac{1}{4} }{(4+cos\theta)*\frac{1}{4} }\\\\r=\frac{2}{4*\frac{1}{4} +cos\theta*\frac{1}{4}}\\ \\r=\frac{\frac{1}{4}*8}{1+\frac{1}{4}cos\theta}[/tex]
This means that the eccentricity (e) = 1/4 and the equation of the directrix is x = ±8
