Home > Graphing > Equations of Rectangular Hyperbola

Equations of Rectangular Hyperbola

Rectangular Hyperbola have horizontal and vertical asymptotes and are in the form y=\frac{a}{x-b} + c

  • b is the value of the x asymptote
  • c is the value of the y asymptote
  • a we calculate by substituting in the values at a point (x_1,y_1)

Consider the graph above.

  • It has a horizontal asymptote y=3 \therefore c=3
  • It has a vertical asymptote x=2 \therefore b=2
  • This gives us y=\frac{a}{x-2}+3
  • It passes through (3,4) so substituting into the above equation gives 4=\frac{a}{3-2}+3 \Rightarrow a=1
  • So y=\frac{1}{x-2}+3
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    Categories: Graphing
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