410 views

### 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)

10 months ago

Answered by Salah, who has applied to tutor A Level Further Mathematics with MyTutor

## Still stuck? Get one-to-one help from a personally interviewed subject specialist

#### 131 SUBJECT SPECIALISTS

£30 /hr

Degree: Mathematics (Bachelors) - Bristol University

Subjects offered:Further Mathematics , Maths

Further Mathematics
Maths

“Hi, I'm Joe, an experienced tutor and a University of Bristol graduate with a first class Degree in Mathematics.”

£20 /hr

Degree: General Engineering (Masters) - Warwick University

Subjects offered:Further Mathematics , Physics+ 2 more

Further Mathematics
Physics
Maths
Economics

“Second year Engineering Student at Warwick University from a low income background who is willing to help children of all backgrounds to excel academically.”

MyTutor guarantee

£26 /hr

Degree: Mathematics (Masters) - York University

Subjects offered:Further Mathematics , Physics+ 1 more

Further Mathematics
Physics
Maths

“I study Maths at York University; I chose York because I loved the lecturers, they made maths fun and easy- that's what I hope to do with all my students!”

£20 /hr

Degree: Economics (Bachelors) - Warwick University

Subjects offered:Further Mathematics , Maths+ 2 more

Further Mathematics
Maths
Economics
-Oxbridge Preparation-

“Hello! I'm Salah, an Economics undergraduate at the University of Warwick. I have a passion for the subject I study, but also loved maths whilst at school and enjoy helping others in any capacity possible. A mentor system at school en...”

MyTutor guarantee

### You may also like...

#### Posts by Salah

f(x) = (4x + 1)/(x - 2). Find f'(x)

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

What characteristics might a perfectly competitive market have? Choose 3 (6 marks)

#### Other A Level Further Mathematics questions

How does proof by induction work?

What is a complex number?

Solve (z-i)+(z+i)+(z-1)+(z-1)

What are differential equations, and why are they important?

We use cookies to improve your site experience. By continuing to use this website, we'll assume that you're OK with this.