Question

Find a polar equation of the ellipse with focus at the pole, eccentricity e= 1/4, and directrix y=4.

Answer 1

because the directrix is a horizontal directrix and the focus at the pole, the equation is\[r = \frac{ed}{1 + e \sin \theta}\]\[e = \frac{1}{4}\]\[d = 4\]\[r = \frac{\frac{1}{4}4}{1 + \frac{1}{4}\sin \theta}\]\[r = \frac{4}{4 + \sin \theta}\]