What are the differences of the two polar equation of two conics $\frac{l}{r}=1+e\cos{\theta}$ and $\frac{l}{r}=1-e\cos{\theta}$

Question

What are the differences of the two polar equation of two conics
$$\frac{l}{r}=1+e\cos{\theta}$$ and $$\frac{l}{r}=1-e\cos{\theta}$$

I have given two figure. What the figure represent and reason behind it. I am unable to understand.

Answer 1

Consider $\theta $ in one sense say anti-clockwise direction in a single setting, after deciding apogee datum or perigee datum. That can be seen from the code of any CAS..($l,p)$ same semi-latus rectum.When $\theta =\pi/2 $ it is same, the plus for decreasing radius vector and minus sign for increasing latus-rectum.

$$ l/r = 1 - \epsilon \cos \theta ;\, l/r = 1 + \epsilon \cos \theta $$

When we notice how Kepler/Newton configured datum point of conics rotation, $\theta$ is symmetric for either direction of rotation and $\pm $ sign in front of $e =0.6 $ to determine whether $\theta$ starts respectively at apogee or perigee of planetary motion.