Question

Q7: Determine the graph of the polar equation r = 12/6+4n cos theta.

Answer 1

Choice B

Explanation:

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

`r=(2)/(1+(2)/(3)cos theta )`

The eccentricity of this conic section is thus 2/3, the coefficient of cos theta. Clearly, the eccentricity is between o and 1 implying that this conic section represents an Ellipse.

Lastly, the ellipse will open towards the left since we have positive cos theta in the denominator. The only graph that meets the conditions is graph B.