Rectangular Hyperbolas

Rectangular Hyperbolas (or Equilateral Hyperbolas) are hyperbolas in the form of: xy = k, where k ¹ 0.

If k = a positive number, then

1) The branches of the hyperbola lie in Quadrant I and III

2) The center is (0, 0)

3) The asymptotes are the x- axis and the y-axis.

4) The Transverse axis of symmetry is: y = x

5) The Conjugate axis of symmetry is: y = -x

6) The Domain is the set of all real numbers, except x 0.

7) The vertices are located where the transverse axis intersects the graph of the hyperbola.

If k = a negative number, then

1) The branches of the hyperbola lie in Quadrant II and IV

2) The center is (0, 0)

3) The asymptotes are the x- axis and the y-axis.

4) The Transverse axis of symmetry is: y = -x

5) The Conjugate axis of symmetry is: y = x

6) The Domain is the set of all real numbers, except x 0.

7) The vertices are located where the transverse axis intersects the graph of the hyperbola.