Let  .

On the axes below, sketch the graph of  ,  labelling all asymptotes with their equations and axis intercepts with their coordinates.   (4 marks)

A graph of the hyperbola    is shown, where and are constants.
 

Find the values of and and hence the graphs -axis intercept.   (2 marks)

The graph of  , where , will always have

1. two vertical asymptotes and one horizontal asymptote.
2. a vertical asymptote with equation and one horizontal asymptote with equation .
3. one horizontal asymptote with equation and only one vertical asymptote with equation .
4. a horizontal asymptote with equation and at least one vertical asymptote.

The graph of the function  , has asymptotes at

1. Find the vertical and horizontal asymptotes of the hyperbola
   

    

    and hence sketch the graph of  .  (3 marks)
   

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2. Hence, or otherwise, find the values of    for which  .  (2 marks)
   

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