This is hot off the press-a question taken from the recently concluded 2011 September Preliminary Examinations of a school in Singapore. It deals with applications of differentiation in the parametric context. Extensive trigonometry is employed here together with the manipulation of surd forms. I have personally worked out everything for your (the student’s) reference.
If you want a real calculus challenge, the problem below should satisfy your appetite. Peace.
The parametric equations of a curve are
where is a positive constant
(i) Find the equation of the tangent to the curve at the point P where .
(ii) The normal to the curve at the point where intersects the axis at . Find the coordinates of and hence show that the area enclosed by the normal at , the tangent and the x-axis is
Frederick Koh is a teacher residing in Singapore who specialises in teaching the A level maths curriculum. He has accumulated more than a decade of tutoring experience and loves to share his passion for mathematics on his personal site www.whitegroupmaths.com.
Mr Koh is also the author of the post Working with summation.
I have created a GeoGebra applet to visualize Question 1 above.