The curve C has polar equation 'r = 3a(1 + cos(x)). The tangent to C at point A is parallel to the initial line. Find the co-ordinates of A. 0<x<pi

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Tangent is parallel, therefore (dy/dx)=0.

Find y:

y = r sin(x) = 3a(1 + cos(x))(sin(x))

Differentiate y with respect to x

dy/dx = 3a[(2cos(x) - 1)(cos(x) + 1)] 

= 0

Solve equation

2cos(x)- 1 = 0

cos(x) = 1/2

x = pi/3

Therefore r = 3a(1 + cos(pi/3))

a = 9a/2

A: (9a/2, pi/3)

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