Answer: Parabola, defined by equal distance to focus and directrix.
- A Circle, defined by constant radius
- B Ellipse, defined by sum of focal distances
- C Parabola, defined by equal distance to focus and directrix
- D Hyperbola, defined by difference of focal distances
Correct answer: C. Parabola, defined by equal distance to focus and directrix
Explanation: Eccentricity exactly equal to 1 uniquely identifies a parabola, where every point is equidistant from the focus and the directrix.
All four conics form a single family distinguished only by eccentricity: a circle is the most "closed" (e=0), an ellipse is an elongated closed curve, a parabola is the borderline open curve (e=1), and a hyperbola has two separate open branches (e>1).
Concept context
Study circles, parabolas, ellipses, and hyperbolas as curves formed by intersecting a plane with a double cone, with their standard equations and key properties.