Question

If the distance from the directrix is 5 units and the distance from the focus is 3 units then what is the name of the conic section?

(a) Ellipse

(b) Parabola

(c) Hyperbola

(d) Circle

This question was posed to me in an international level competition.

The origin of the question is Basics of Conic Sections in section Curves used in Engineering Practice of Engineering Drawing

Answer 1

The correct choice is (a) Ellipse

To explain I would say: Eccentricity is defined as the ratio of the distance from the focus to the distance from the directrix and it is denoted by e. Hence, by definition, e = 3 ÷ 5 = 0.6. Hence the conic section is called an ellipse.