Central rectangle

Definition

A central rectangle is a rectangle whose sides are parallel to the asymptotes of a hyperbola and its vertices lie on the hyperbola. It helps in visualizing the geometric properties of the hyperbola.

5 Must Know Facts For Your Next Test

1. A central rectangle's sides are aligned with the asymptotes of the hyperbola.
2. The center of the rectangle coincides with the center of the hyperbola.
3. The diagonals of a central rectangle intersect at the center of the hyperbola.
4. The vertices of a central rectangle touch the hyperbola at four points, two on each branch.
5. A central rectangle can be used to derive important properties such as slopes and equations of asymptotes.

Review Questions

• What is the relationship between a central rectangle and the asymptotes of a hyperbola?
• How do you locate the vertices of a central rectangle on a hyperbola?
• What geometric properties can be derived from a central rectangle?

Related terms

Hyperbola: A type of conic section formed by intersecting a double cone with a plane in such a way that both halves are symmetrical.

Asymptote: A line that approaches a curve arbitrarily closely as one or both coordinates tend to infinity.

Conic Sections: Curves obtained by intersecting a right circular cone with a plane at different angles and positions.