Hyperbolas

Question

Find the vertical and horizontal asymptotes of the hyperbola y= (x-2)/(x-4) and hence sketch the graph.

Answer 1

y = (x-2)/(x-4)

 

Denominator = 0 when x = 4, Numerator ≠ 0 when x = 4.  So, vertical asymptote is:  x = 4.

 

The numerator and denominator have the same degree.  So, to find the horizontal asymptote, divide the leading coefficients.  Horizontal asymptote is y = 1.