Which term describes the ratio that characterizes the shape of a conic section?

Which term describes the ratio that characterizes the shape of a conic section?

• A. Diameter
• B. Radius
• C. Eccentricity
• D. Focus

Answer: (C)

Eccentricity is the quantity that encodes how stretched a conic is. It’s the fixed ratio of the distance from any point on the curve to the focus, divided by the distance to the directrix. This constant ratio determines the shape: if e is less than 1, you get an ellipse (a circle is a special case where e is 0); if e equals 1, you get a parabola; if e is greater than 1, you get a hyperbola. Diameter and radius describe size, not the overall shape of all conics, and the focus is a defining point, not the ratio itself.

Eccentricity is the quantity that encodes how stretched a conic is. It’s the fixed ratio of the distance from any point on the curve to the focus, divided by the distance to the directrix. This constant ratio determines the shape: if e is less than 1, you get an ellipse (a circle is a special case where e is 0); if e equals 1, you get a parabola; if e is greater than 1, you get a hyperbola. Diameter and radius describe size, not the overall shape of all conics, and the focus is a defining point, not the ratio itself.