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)
