Applications of Conic Sections

There are many applications of conic sections in both pure and applied mathematics. Here we shall discuss a few of them. The orbits of planets and satellites are ellipses. Ellipses are used in making machine gears.


Arches of bridges are sometimes elliptical or parabolic in shape. The path of a projectile is a parabola if motion is considered to be in a plane and air resistance is neglected. Parabolas are used in the design of parabolic mirrors, searchlights, and automobile headlights.


Hyperbolas are used in combat in “sound ranging” to locate the position of enemy guns by detecting the sound of gunfire. If a quantity varies inversely as another quantity, such as pressure and volume of Boyle’s law for a perfect gas at a constant temperature, the graph is a hyperbola.


Some astronomical bodies revolve around the sun in a hyperbolic path. One interesting application is if a torch light is placed against the wall its shadow on the wall forms a hyperbolic curve.