Consider the hyperbola    and the circle  , where is a constant.

1. Show that the -coordinates of any points of intersection of the hyperbola and circle are zeros of the polynomial  .  (1 mark)
   

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2. The graphs of    for    and  are shown.
    

1. By considering the given graphs, or otherwise, find the exact value of    such that the hyperbola    and the circle    intersect at only one point.  (3 marks)
   

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