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

6803 Views

See similar Further Mathematics A Level tutors

Related Further Mathematics A Level answers

All answers ▸

Use De Moivre's Theorem to show that if z = cos(q)+isin(q), then (z^n)+(z^-n) = 2cos(nq) and (z^n)-(z^-n)=2isin(nq).


Why is the integral of 1/sqrt(1-x^2)dx = sin^{-1}(x)?


The point D has polar coordinates ( 6, 3π/4). Find the Cartesian coordinates of D.


Show that the set of real diagonal (n by n) matrices (with non-zero diagonal elements) represent a group under matrix multiplication


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

MyTutor is part of the IXL family of brands:

© 2025 by IXL Learning