Determine the eccentricity, the type of conic, and the directrix for r=6/1+2cos theta.

Answer:Option cStep-by-step explanation:The general polar form of the conic with cosine in the denominator is:[tex]r=\frac{ep}{1+ecos(\theta)}[/tex]Comparing the given equation (Denominator) with the general equation, we can write:e = 2This means eccentricity = 2. Since eccentricity is greater than 1, the given conic is a hyperbola.The equation of directrix is x = pComparing the numerators of general and given equation, we can write:ep = 6Using the value of e, we get p = 3Therefore, equation of directrix is x =3Hence option c is the correct answer.