Elements of a Hyperbola

2.0
1.5

Transverse Axis Length:

Conjugate Axis Length:

Eccentricity (e):

Asymptote Slopes:

This interactive graph illustrates the key components of a hyperbola. You can choose between a horizontal or vertical orientation and adjust the 'a' (semi-transverse) and 'b' (semi-conjugate) values using the sliders.

  • Center: The midpoint of the hyperbola, located at $(0,0)$.
  • Foci: Two fixed points outside the hyperbola. The absolute difference of the distances from any point on the hyperbola to the two foci is constant.
  • Vertices: The points on the hyperbola that intersect the transverse axis.
  • Covertices: The points that define the conjugate axis, perpendicular to the transverse axis.
  • Transverse Axis: The line segment connecting the vertices. Its length is $2a$ for horizontal, $2b$ for vertical.
  • Conjugate Axis: The line segment perpendicular to the transverse axis, passing through the center. Its length is $2b$ for horizontal, $2a$ for vertical.
  • Latera Recta: Chords perpendicular to the transverse axis passing through the foci.
  • Directrices: Two lines perpendicular to the transverse axis, related to the foci and eccentricity.
  • Asymptotes: Lines that the hyperbola approaches but never touches.

The graph automatically adjusts to fit the screen size, ensuring a clear view of all elements.