NJC/2013/I/Q8 Finding Area of Parametric Equations

The curve C has parametric equations

(i) Sketch C, labeling all axial intercepts(s).

(ii) Find the equation of the tangent to the curve when t=1, leaving your answer in terms of e. 

(iii) The normal to the curve C at point  is parallel to the x-axis and intersects the y-axis at point S (0,s), where s<1. Find the exact value of p. 

(iv) Find the area of the region bounded by the curve C and the y-axis. 

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