2.51: Tangent to a quadratic and shaded area

The diagram shows the curve intersecting the positive -axis at the point . The line is a tangent to the curve at the point . Find
(i)[2]
the coordinates of ,
(ii)[3]
the value of ,
(iii)[2]
the coordinates of ,
(iv)[5]
the area of the shaded region, showing all your working.
