Question

What are the parts of a hyperbola?

Answer 1

The parts of a hyperbola:

The standard equation of a hyperbola is $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$.

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 $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$are $(ae,0)$ 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: $e=\sqrt{1+\frac{b^2}{a^2}}$.