The diagram shows the curve C with y parametric equations (0,2a) x =-2a cot t, y= 2a sin? t, where 0
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![The diagram shows the curve C with
y
parametric equations
(0,2a)
x =-2a cot t, y= 2a sin? t,
where 0<t<r and a is a positive
constant.
y = 0
dy
= 2sin' t cost.
dr
(i)
Show that
(ii) Hence find, in terms of a, the equation of the tangent 1 to C which is parallel to the
х-ахis.
(iii) A point P on C has parameter t =-. Given that the tangent to C at P meets l at the
3
point Q and the point R is the foot of the perpendicular from P to l, find the exact area
of triangle PQR in terms of a.
[(ii) y = 2a, (ii)
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