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Question

What are the parts of a hyperbola?


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Solution

The parts of a hyperbola:

The standard equation of a hyperbola is x2a2-y2b2=1.

The following are the parts of a hyperbola:

  • Foci of a hyperbola: Foci of the hyperbola are points on the axis of the hyperbola. The two foci of the hyperbola x2a2-y2b2=1are (ae,0) and (-ae,0).
  • Focal length: Distance between the two foci of the hyperbola.
  • Transverse axis: The transverse axis is the segment that goes through the two foci and the center of the hyperbola.
  • Conjugate axis: The conjugate axis is the line passing through the center of the hyperbola and perpendicular to the transverse axis.
  • Center: The midpoint of the line joining the two foci is called the center of the hyperbola.
  • Vertices: The vertices are the points of intersection of the hyperbola with the transverse axis.
  • Axes of symmetry: Axis of symmetric is a line that divides a hyperbola into two equal parts or creates a mirror image. There are two axes of symmetry for a hyperbola.
  • Semi-major axis: The semi-major axis of a hyperbola is one-half of the distance between the two foci of the hyperbola.
  • Semi-minor axis: The semi-minor axis is a line segment that is perpendicular to the semi-major axis. One end of the semi-major axis is the center of the hyperbola.
  • Asymptotes: The asymptotes of a hyperbola are straight lines that the curve approaches as the values of the independent variable increase.
  • Eccentricity: for any point on the hyperbola, the ratio of its distance from the foci and its distance from the directrix is a constant value called the eccentricity of hyperbola and is greater than 1. Formula: e=1+b2a2.

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