2006 SQA Higher Maths: paper 2 no.3: Tangent to a curve

Finding the equation of a tangent to a parabola. Showing a given line is a tangent to a parabola.. This is rather lengthy as several techniques are shown. The main technique is shown first for each part. The alternative for each part is shown separately at the end. Instructional exercise consisting of question 3 from paper 2 of the 2006 SQA Higher Mathematics exam. Set out in stages of 'try then check' the worked solution to each part of the question. Including indications of where each mark is allocated, and the requirements for that mark, according to the marking scheme.