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
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)
SS
Answered by Salah S. • Further Mathematics tutor
7990 Views
See similar Further Mathematics A Level tutorsRelated Further Mathematics A Level answers
All answers ▸Using a Taylor's series or otherwise; derive Euler's Formula
The plane Π contains the points (1, 2, 3), (0, 1, 2) and (2, 3, 0). What is the vector equation of the plane? and what is the cartesian equation of the plane?
Find the area of the surface generated when the curve with equation y=cosh(x) is rotated through 2 pi radians about the x axis, with 2<=x<=6
Find the stationary points of the function z = 3x(x+y)3 - x3 + 24x