The diagram illustrates the design for part of a roller-coaster track. The section    is a straight line with slope 1.2, and the section    is a straight line with slope  – 1.8. The section    is a parabola  . The horizontal distance from the  -axis to    is 30 m.
 

In order that the ride is smooth, the straight line sections must be tangent to the parabola at    and at  .  

1. Find the values of    and    so that the ride is smooth.   (3 marks)
   

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2. Find the distance  , from the vertex of the parabola to the horizontal line through  , as shown on the diagram.     (2 marks)
   

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