Question

Q9: Determine e, k, and identify the type of conic for r= 12/7-cos theta .

Answer 1

eccentricity; e = 1/7

k = 12

Conic section; Ellipse

Answer 2

eccentricity; e = 1/7

k = 12

Conic section; Ellipse

Explanation:

The first step would be to write the polar equation of the conic section in standard form by multiplying the numerator and denominator by 1/7;

`r=((12)/(7) )/(1-(1)/(7)cos theta)`

The polar equation of the conic section is now in standard form;

The eccentricity is given by the coefficient of cos theta in which case this would be the value 1/7. Therefore, the eccentricity of this conic section is 1/7.

The eccentricity is clearly between 0 and 1, implying that the conic section is an Ellipse.

The value in the numerator gives the value of k; k = 12