Question

If the distance from the focus is 10 units and the distance from the directrix is 30 units, then what is the name of the conic?

(a) Circle

(b) Parabola

(c) Hyperbola

(d) Ellipse

I got this question in an international level competition.

My question comes from Basics of Conic Sections in section Curves used in Engineering Practice of Engineering Drawing

Answer 1

Correct answer is (d) Ellipse

The explanation is: Eccentricity is defined as the ratio of the distance from the focus to the distance from the directrix. Hence from the formula of eccentricity, e = 10 ÷ 30 = 0.3333. Since the value of eccentricity is less than one the conic is an ellipse.