Conic sections are a group of curves which are generated by slicing a cone with a plane. If the plane is tilted parallel to the slope of the cone, the cut produces a parabola. When a parabola is expressed in Cartesian coordinates, the equation is a second order polynomial. This curve is commonly found in nature, engineering applications and architecture.
             The study of projectile motion is a real life application of the parabolic conic section. Soccer balls, divers, missiles and airplanes follow perfect parabolic trajectories if the air resistance is neglected. Garden hoses and fountains discharge water droplets whose trajectory is also described by a parabolic motion (Serway & Jewett, 2007). The projectile (ball, airplane, droplet) moves under the influence of gravity, which for simplicity is assumed to be constant. Thus, it is possible to derive an expression for the height of the projectile as a function of the horizontal position. It turns out to be a second order polynomial that represents a parabola (see Appendix A for an example of projectile motion). Projectile motion was first studied by Galileo in the 17th century. At that time, it was useful to determine the firing of a cannonball so as to reach enemy targets. A similar technique is used today for launching long range missiles, but the computed trajectory takes into account slight variations in gravity and changes due to air drag.
             Parabolic mirrors are commonly found in optical instruments such as cameras, telescopes, and microscopes. The surface of the mirror has a parabolic form. Parabolic mirrors ensure that the image is not blurred as it eliminates aberration, i.e. reflected rays should only pass through a single focal point. This type of mirrors are expensive as they are not easy to manufacture. Vehicle headlights also have a parabolic curvature. If a bulb is located exactly at the focus of a parabolic mirror, the rays are reflected parallel to the axis of the para...