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📐 Mathematics  ·  Conic Sections  ·  JEE

The eccentricity of a conic is found to be exactly 1. Which type of conic must it be, and what defines its shape uniquely?

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.

The Four Conics by EccentricityCircle (e=0)Ellipse (0<e<1)Parabola (e=1)Hyperbola (e>1)

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.

Read the full Conic Sections notes →