You Answered: Ellipse
YES, you are correct!
An ellipse is a special sort of squashed circle, in fact a circle seen from an angle. The curved path of a projectile moving in an inverse-square force field like the earth's gravity is an ellipse, as Isaac Newton first showed. This connected Kepler's First Law, that the orbits of planets are ellipses, with Newton's mechanics. Of course, your ball traces out only a very small part of an ellipse, before it hits the ground, splat. The full ellipse encloses the center of the earth, as shown in the diagram, which exaggerates the proportions so you can see the concept. The orbits of the planets and moon are nearly circular, but your ball's ellipse is nearly flat. Extra credit: compute the approximate width of the ellipse.
Take a look at the other answers on this page.
You answered:Parabola
YES, you are correct!
The vertical height of the ball changes as the square of time, while the horizontal distance of the ball
from the release point increases uniformly with time. This is
Galileo's result, explained by Newton. This was significant at the time for pointing cannon,
as this
Museum exhibit shows.
Here is a real-time Java simulation of a cannon, and
here's a
non-Java animation of a cannon with physics discussion by a high school teacher. The
clouds called "mares'
tails" are an example of falling parabolas with a twist.
Fireworks are Java parabolas in all directions.
Of course, a parabolic path is an
approximation, assuming among other things that the pull of gravity is down,
meaning parallel at all points on the path, instead of ever so slightly angled to the earth's center. If you think
that's always a silly distinction on the earth's surface, consider that bridge towers
are measureably not parallel: the tops of the towers of the
Verrazano Narrows Bridge in New York City are almost two inches further apart than their bases.
Extra credit: compute this. And by the way, is the
shape taken by the cables of a
suspension bridge a parabola? How about just an isolated
cable suspended from its ends? Galileo
thought it was.
Did you know that there is only one parabolic shape,
not a family of shapes as with the other answer choices on this page?
Take a look at the other answers on this page.
You answered: Hyperbola
YES, you are correct!
That is, if you have a very strong arm...if the ball is moving fast enough it will follow a hyperbola and leave the
earth permanently. 
Escape velocity at the earth's surface is about seven miles per second.
(If you chose this answer you are sentenced to compute that value ;)
Some comets and a few
spacecraft are on hyperbolic trajectories and are leaving the solar system.
Of course, your ball may burn up in the atmosphere before it escapes...Take a look at the other answers on this page.
You answered: None of the Above
YES, you are correct!
The air through which the ball is moving will significantly change the ball's motion from what it would be in a
vacuum, say on the moon. 
Some of you may remember Apollo 14 astronaut Alan Shepard's first
golf shot on the moon.
(warning: 4 MB gzipped movie file!)
The resulting motion through the air is not one of the simple curves in the list of answers. Of course, problems like this in
elementary physics usually want you to neglect such complicating factors. Any real world situation must be
modeled by an approximation: the only issue is how accurate the approximation. Yale physics
professor Robert Adair, sometime "Physicist to the National League," has a book
The Physics of Baseball 2nd Ed,
that talks about a lot of these sort of issues in an approachable way. The
graph is adapted from his book, to show the trajectory
for a batted ball at different speeds. The ball starts from 0, flies up to the right, and falls back to ground.
Notice the ball falls more steeply than it rises,
while a parabola, which is close to the motion in vacuum, rises and falls the same way
("is symmetric around its peak" if you know the jargon).
This is because the air is slowing the ball down: the horizontal part of the velocity is
continuously decreasing and is less during the fall than the rise. Hence the ball doesn't
go as far horizontally during the fall, and the fall is steeper. Here's a
Java simulation of a projectile with air resistance.
The effect of air on motion is complex:
you can throw a curve ball because of the
Magnus Effect,
which can be investigated in a student lab or
on a computer.
Major league fastballs and
breaking balls.
Here's an extract from The Physics of Golf.
Not involving air, billiard ball motion is often given as an example of the particularly simple, but the reality is otherwise:
understand why the
angle of ball collision
isn't what you might expect. More approachably,
the Exploratorium has an online exhibit of Sports Science.
Take a look at the other answers on this page.
Track and field throwing, and Scottish things to throw, including instructions.
Capital High students' papers on throwing.
"Everybody has won, and all must have prizes."
The Dodo, to Alice
The catapult is from this graphics page.
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