Johannes Kepler
Yes; the circle is a special case of an ellipse.
For Ellipse: The 2 circles made using the the ellipse center as their center, and major and minor axis of the ellipse as the dia.For Hyperbola: 2 Circles with centers at the center of symmetry of the hyperbola and dia as the transverse and conjugate axes of the hyperbolaRead more: eccentric-circles
The ancient Greeks used Ptolemy's theory, based on circles, that was good enough for the accuracy needed at the time. Later Kepler in the 16th century discovered that an ellipse is a better model of a planetary orbit. In modern times it has been discovered that an ellipse is an approximation and that true orbits have no simple description. But the ellipse is a good enough model for many purposes.
No. A circle is a special kind of ellipse.
Copernicus's Sun-centred (heliocentric) model of the planets' orbits used circles and epicycles, as the Ptolemaic model had done although the older model had the Earth at the centre. Kepler took the heliocentric idea and used it as the basis for extended calculations on the orbit Mars using new observations and measurements of unprecedented accuracy by his employer, Tycho Brahe. Mars's orbit had just enough eccentricity (9%) to allow a difference to show up between the earlier model and Kepler's new discovery of eliptical orbits. Kepler also found that the other planets had elliptical obits, but the eccentricity was lower. He developed his three laws of planetary motion now known as Kepler's laws.
"Elliptical" means they look like ellipses.
The outside of the circle is always the same distance from the centre. The outside of an ellipse is not the same distance from the centre all the way round.
two circles and an ellipse
The whole ellipse shifts down by 6 units.
As the foci of an ellipse move closer together, the ellipse becomes more circular in shape. When the foci coincide, the shape is a circle. Note that circles are a subset of ellipses.
The path is called an orbit, and it's shaped like an ellipse.
An ellipse, or egg-shaped. Orbits are not very egg-shaped, though . . . they are almost circles.