An ellipse has 2 foci. They are inside the ellipse, but they can't be said to be at the centre, as an ellipse doesn't have one.
Most orbits are elliptical; all NATURAL orbits are. There are two foci, or focuses, to an ellipse. The distance between the foci determines how eccentric, or non-circular, they are. If the two foci are in the same place, then the ellipse becomes a circle. So a circular orbit would have only one focus.
The eccentricity of an ellipse is a number related to how "egg-shaped" it is ... the difference between the distance through the fat part and the distance through the skinny part. That's also related to the distance between the 'foci' (focuses) of the ellipse. The farther apart the foci are, the higher the eccentricity is, and the flatter the ellipse is. Comets have very eccentric orbits. When the two foci are at the same point, the eccentricity is zero, all of the diameters of the ellipse have the same length, and the ellipse is a circle. All of the planets have orbits with small eccentricities.
All natural orbits are ellipses. We can force an artificial satellite into a spherical orbit, but it won't STAY there without occasional adjustments. The "primary body" - in this case, the Sun - is at one of the two focuses (foci) of the orbit. If the focus is very close to the "center" of the ellipse, then the eccentricity of the orbit (how much it varies from a perfect circle) is close to zero.
The orbit of a planet is not a circle with the sun at the center. It's an ellipse with the sun at one focus. An ellipse is an 'egg shape', or 'oval', or 'squashed circle'. It has two foci (focuses) and neither one is in the center. So you can easily see that as the planet moves along the ellipse, its distance from the sun changes, and there is a minimum distance (perihelion) and a maximum distance (aphelion). Those don't change unless the shape of the ellipse changes, and the only way that happens is through the gravitational influence of the other planets, which is relatively tiny over the course of many millennia.
The path itself is called its orbit. The shape is an ellipse, with the sun sitting at one of the foci.
A circle is an ellipse with an eccentricity of zero. Both foci of that ellipse are at the same point. In the special case of the circle, that point is called the "center".
Two
No. Both foci are always inside the ellipse, otherwise you don't have an ellipse.
No. Both foci are always inside the ellipse, otherwise you don't have an ellipse.
No. Both foci are always inside the ellipse, otherwise you don't have an ellipse.
No.
No.
No.
An ellipse has two lines of mirror symmetry: the line that includes the two foci of the ellipse and the perpendicular bisector of the segment of that line between the two foci.
The length of the semi-major axis multiplied by the eccentricity.
An ellipse, a hyperbola.
Foci.