What is conic section essay?
What is conic section essay?
Conic sections are the various gemetric figures created by the interection of a plane. They are among the oldest curves in history and is one of the oldest area of study for mathmaticians. Euclid studied them and Appollonius reinforced and expanded previous results of conics into a book he named Conic Sections.
What is conic section in your own words?
A conic section (or simply conic) is a curve obtained as the intersection of the surface of a cone with a plane; the three types are parabolas, ellipses, and hyperbolas. A conic section can be graphed on a coordinate plane. Every conic section has certain features, including at least one focus and directrix.
Why is conic section important?
The study of conic sections is important not only for mathematics, physics, and astronomy, but also for a variety of engineering applications. The smoothness of conic sections is an important property for applications such as aerodynamics, where a smooth surface is needed to ensure laminar flow and prevent turbulence.
How is conic section related to real life?
What are some real-life applications of conics? Planets travel around the Sun in elliptical routes at one focus. Mirrors used to direct light beams at the focus of the parabola are parabolic. Parabolic mirrors in solar ovens focus light beams for heating.
What is the reflective property of parabola?
Thus the reflection property tells us that any ray parallel to the axis of the parabola will bounce off the parabola and pass through the focus.
Who is said to have written four books on conics but were lost as well?
Euclid (fl. 300 BCE) is said to have written four books on conics but these were lost as well.
What are some real life examples of ellipses?
Many real-world situations can be represented by ellipses, including orbits of planets, satellites, moons and comets, and shapes of boat keels, rudders, and some airplane wings. A medical device called a lithotripter uses elliptical reflectors to break up kidney stones by generating sound waves.
Why is hyperbola important in real life?
Scientists and engineers established radio stations in positions according to the shape of a hyperbola in order to optimize the area covered by the signals from a station. LORAN allows people to locate objects over a wide area and played an important role in World War II.
What is the importance of ellipse?
The ellipse is one of the four classic conic sections created by slicing a cone with a plane. The others are the parabola, the circle, and the hyperbola. The ellipse is vitally important in astronomy as celestial objects in periodic orbits around other celestial objects all trace out ellipses.
How are parabolas used in headlights?
Headlights: The optical property is also responsible for parabola-shaped unidirectional lights, such as car headlights. If a bulb is placed at the focus of a parabolic mirror, the light rays reflect off the mirror parallel to each other, making a focused beam of light.
What is the history of the conic section?
Historical introduction. Conic sections are among the oldest curves, and is one of the oldest mathematics subjects studied rigorously. The conics were discovered by Menaechmus (a Greek, c. 375-325 BC) who was a pupil of Plato and Exodus in an attempt to solve the famous problem duplicating the cube.
What is the general equation of a conic section?
The general equation of a conic section can be written as Ax2 + Bxy + Cy2 + Dx + Ey + F = 0 however, every conic section has its own equations especially in computing for their vertices that helps in determining the kind of conic section given by a particular equation. The type of section can also be found from the equation B2 – 4ac.
What is the minor axis of a conic section?
Alternative characterization of conic sections. The chord of the ellipse joining the vertices is called the major axis, and the chord through the center perpendicular to the major axis is called the minor axis. Identify the fixed points as A and B (these are the foci) and use GSP to create an ellipse.
What is the difference between directrix and eccentricity of conic section?
A directrix is the line that serves to define the conic section as the set of all the points that satisfies a certain condition together with the focus. On the other hand the eccentricity of a conic section is the distance to the focus and the directrix.
