This indicator is named the Stop And Reverse, SAR, Parabolic. A parabola is one of the three possible conic sections (others being ellipse [the circle is a special case of an ellipse] and hyperbola). Why is this indicator named parabolic?
The next question... What exact parameters in the MQL4 Parabolic SAR indicator code could make it an ellipsoidal shape/surface or a hyperbolic if indeed some set parameters make it parabolic?
The aim of my question(s) have to do with a question of mathematical eccenntricity (from wikipedia on conic sections):
Eccentricity

Ellipse (
e=1/2),
parabola (
e=1)
and
hyperbola (
e=2) with fixed focus
F and directrix.
The four defining conditions above can be combined into one condition that depends on a fixed point F (the focus), a line L (the directrix) not containing F and a nonnegative real number e (the eccentricity). The corresponding conic section consists of all points whose distance to F equals e times their distance to L. For 0 < e < 1 we obtain an ellipse, for e = 1 a parabola, and for e > 1 a hyperbola.
The objective is for research and development of a 'SAR ellipsoid' and 'SAR Hyberbolic' indicators. It is further for development of a (continuous [24hrs]) 'time series wobble' type of model that is based on the physical phenomenon of a rattleback (rattleback from wikipedia):
A rattleback, also known as an "anagyre", "celt",
"Celtic stone", "rebellious celt", "rattlerock", "spin bar", "wobble
stone" or "wobblestone" and by the product names "ARK," "Bizzaro
Swirls," "RATTLEBACKS," "Space Pet" and "Space Toy," is a
semi-ellipsoidal top
which will spin on its axis in a preferred direction. But, if spun in
the opposite direction, it becomes unstable, "rattles", stops and
reverses its spin to the preferred direction.
Behold the mysterious celt, with a property that amuses. One way it will spin, the other way it refuses.
This spin-reversal motion seems, at first sight, to violate the angular-momentum conservation law of physics...