(q10) determine the eccentricity, the type of conic, and the directrix for r = 11/ 6 - 5 cos theta.

Choice C

eccentricity = 5/6

conic section; ellipse

directrix; x = -11/5

Step-by-step explanation:

The first step is to write the polar equation in standard form by dividing both the numerator and denominator by 6;

The eccentricity of the conic section is the coefficient of cos theta, thus;

e = 5/6

Since e lies between 0 and 1, the conic section is an ellipse.

To determine the equation of the directrix, we use the equation;

e*d = 11/6

5/6 *d = 11/6

d = 11/5

Since the conic section opens towards the right, the equation of the directrix becomes;

x = -11/5