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📐 Mathematics  ·  Conic Sections  ·  JEE

A general second-degree equation represents a circle when the coefficients of x² and y² are equal and the xy term is:

Answer: absent (zero).

  • A absent (zero)
  • B clearly present
  • C strongly negative
  • D extremely large

Correct answer: A. absent (zero)

Explanation: A circle needs equal x² and y² coefficients and no xy (cross) term.

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 →