What is "circle at infinity"

Infinity \In*fin"i*ty\, n.; pl. Infinities. [L. infinitas; pref. in- not + finis boundary, limit, end: cf. F. infinit['e]. See Finite.]

1. Unlimited extent of time, space, or quantity; eternity; boundlessness; immensity.
   --Sir T. More.

   There can not be more infinities than one; for one of them would limit the other.
   --Sir W. Raleigh.

2. Unlimited capacity, energy, excellence, or knowledge; as, the infinity of God and his perfections.
   --Hooker.

3. Endless or indefinite number; great multitude; as an infinity of beauties.
   --Broome.

4. (Math.) A quantity greater than any assignable quantity of the same kind.

   Note: Mathematically considered, infinity is always a limit of a variable quantity, resulting from a particular supposition made upon the varying element which enters it.
   --Davies & Peck (Math. Dict.).

5. (Geom.) That part of a line, or of a plane, or of space, which is infinitely distant. In modern geometry, parallel lines or planes are sometimes treated as lines or planes meeting at infinity.

   Circle at infinity, an imaginary circle at infinity, through which, in geometry of three dimensions, every sphere is imagined to pass.

   Circular points at infinity. See under Circular.