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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ISBN:9780470458365
Author:Erwin Kreyszig
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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)
3/3
Transcribed Image Text: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) 3/3
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