Undergrad Angle at which cardioid hits the x-axis

[Any Help]

How can we find the angle at which 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.

 

[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...

 

[BvU]

Hello,
Concerning my post, no it's not a homework. I only need a method to help me in my exam while drawing. Without going to the long way converting to XY equation the find derivative and that stuff.

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 )