Question

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

Answer 1

the answer is C

Explanation:

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Answer 2

Option c

Explanation:

The general polar form of the conic with cosine in the denominator is:

`r=(ep)/(1+ecos(\theta))`

Comparing the given equation (Denominator) with the general equation, we can write:

e = 2

This means eccentricity = 2. Since eccentricity is greater than 1, the given conic is a hyperbola.

The equation of directrix is x = p

Comparing the numerators of general and given equation, we can write:

ep = 6

Using the value of e, we get p = 3

Therefore, equation of directrix is x =3

Hence option c is the correct answer.