Determine the eccentricity, type of conic, and the directrix. r=7/(4-2cos(θ))

Answer 1

r = 7/(4 - 2cos(2θ));

Polar equation is r = ed/(1 - ecosθ).

In our case r = 7/[4(1 - 1/2cosθ)];

From here exentricity e = 1/2 ellipse; ed = 7/4 = 1/2·7/2 = e·7/2; so d = 7/2 and equation of directrix x = - 7/2