Hyperbola

Definition

A hyperbola is a type of conic section formed by the intersection of a plane and a double-napped cone. It consists of two disconnected curves called branches.

5 Must Know Facts For Your Next Test

1. A hyperbola has two foci and two vertices.
2. The standard form equation for a horizontal hyperbola is $\frac{(x-h)^2}{a^2} - \frac{(y-k)^2}{b^2} = 1$.
3. The transverse axis connects the vertices, while the conjugate axis connects the co-vertices.
4. Asymptotes of a hyperbola are lines that the branches approach but never touch; they intersect at the center of the hyperbola.
5. In polar coordinates, a hyperbola's equation can be given as $r = \frac{ed}{1 + e \cos \theta}$ where $e > 1$.

Review Questions

• What is the standard form equation for a vertical hyperbola?
• How do you determine the foci of a hyperbola given its equation?
• What are asymptotes in relation to a hyperbola?

Related terms

Ellipse: A conic section formed by intersecting a plane with a single-napped cone, resulting in an oval shape.

Parabola: A conic section formed by intersecting a plane parallel to one generator of the cone, creating a U-shaped curve.

Conjugate Axis: The line segment perpendicular to the transverse axis that passes through the center and whose endpoints are co-vertices.