Center of a hyperbola

Definition

The center of a hyperbola is the midpoint of the line segment joining its two foci. It is also the point where the transverse and conjugate axes intersect.

5 Must Know Facts For Your Next Test

1. The coordinates of the center of a hyperbola can be found as the midpoint between its foci, represented as $(h,k)$.
2. In standard form equations of hyperbolas, $\frac{(x-h)^2}{a^2} - \frac{(y-k)^2}{b^2} = 1$ or $\frac{(y-k)^2}{a^2} - \frac{(x-h)^2}{b^2} = 1$, $(h,k)$ represents the center.
3. The center is equidistant from each vertex and each focus.
4. Shifting a hyperbola horizontally or vertically changes its center but retains its overall shape.
5. For horizontal hyperbolas, the transverse axis runs through the center horizontally; for vertical hyperbolas, it runs vertically.

Review Questions

Related terms

Foci:

Two fixed points on either side of a hyperbola's center used to define and construct it.

Transverse Axis:

The line segment that passes through both vertices and foci of a hyperbola; it intersects at the center.

Conjugate Axis:

The line segment perpendicular to the transverse axis at the center, whose endpoints are called co-vertices.