Question

Determine the eccentricity, the type of conic, and the directrix for r=59+6cos(θ).

a) Eccentricity: 6, Type: Hyperbola, Directrix: θ= π/6
b) Eccentricity: 9, Type: Ellipse, Directrix θ=3π
c) Eccentricity: 6, Type: Circle, Directrix: θ=6π
d) Eccentricity: 9, Type: Parabola, Directrix: 3θ= π3

Answer 1

The eccentricity is 6, the type of conic is an ellipse, and the directrix cannot be determined.

Step-by-step explanation:

The shape (roundness) of an ellipse depends on how close together the two foci are, compared with the major axis. The ratio of the distance between the foci to the length of the major axis is called the eccentricity of the ellipse. In the given equation, r=59+6cos(θ), the eccentricity is 6, which means the path represented is ellipse.

The directrix of an ellipse is a line that is equidistant from the two foci. In this case, the directrix cannot be determined from the given equation.