Rectangular Hyperbolas

 

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Rectangular Hyperbolas

 

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

 

 

 

 

 

 

 

 

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