# I Angle at which cardioid hits the x-axis

1. Dec 4, 2016

### Any Help

How can we find the angle at wich the curve of equation : r=b + acosθ hits the x-axis.
I want a fast way or method since I only need it to plot the graph well. I'm only asked to plot the curve well and pay attention to the angle at which the curve hits the x-axis and not to calculate and write how I got it.

2. Dec 4, 2016

### BvU

Looks like homework to me ... needs your attempt at solution. You know, PF rules and all that.

By the way, acosθ is slightly ambiguous...

Last edited: Dec 4, 2016
3. Dec 4, 2016

### BvU

Fair enough.

So what you want is $\displaystyle {dy\over dx}$ at y = 0, right ?
Write $\ y = y(r,\theta) = y(\theta)\$ and $\ x = x(r,\theta) = x(\theta)\$
Take derivatives
Divide
On the way you see you need derivatives at $\theta = 0, \ \theta = \pi$ that are trivial.
The other two or four (at $x=0$ ) require some work.
I know of no quicker way.
(except using excel to cheat drawing the pictures )