In order to reflect all light of an object located at
infinity into a single point, the mirror should have a
paraboloidal shape. The object should then be located on the
optical axis of the mirror.
The paraboloidal shape is obtained by rotating a parabolic around its axis.
It is usually called "parabolic"
The formula for a parabolic curve is:
In the figure below the wavefront comes in from the right. The shape of the mirror must be such that all "light ray's" travel the same distance from the wavefront to the focal point. The only mirror shape which performs this is the paraboloidal.
Since there is no such thing as a free lunch, there is a disadvantage. Objects off-axis will not focus in a single point, they will produce a kind of V-shape. This is known as "coma".
In the above figure the wavefront is drawn through the focal point, this is a mere coincidence and has no implications. It should also be noted that the mirror curvature is not corresponding to the focal length.