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📐 Mathematics  ·  Conic Sections  ·  JEE

The line y = x + c is tangent to the circle x² + y² = 2 when c equals:

Answer: ±2.

  • A ±1
  • B ±2
  • C ±√2
  • D ±4

Correct answer: B. ±2

Explanation: Tangency requires c² = r²(1 + m²) = 2·2 = 4, so c = ±2.

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 →