Applications of conic sections•Parabola•Ellipse•Circle•Hyperbola

Submitted To: Ma’m Sapna MakhdoomSubmitted By:

• Irum GulBahar 02• Hajrah Majeed 14• Humera Yousaf 19• Amna Ayub 21

Topic: Applications of Conic Sections in Real/Daily LifeSession: 2013-17Department: Mathematics

Mirpur University Of Science & Technology(MUST)

• Dedication:We dedicate this project name “ Applications of

Conic sections in real Life” to our parents and Family members.

• AbstractIn this project we discuss “Applications of Conic

Sections in Real Life”. There are a lot of uses of conic sections in real life. we have

discussed only some.

• AcknowledgementFirst of all we would like to thank Allah almighty

for making this project possible for us. Then special thanks to Ma’m Sapna Makhdoom for helping us in completing this project

Definition:

– Conic sections are the curves which can be derived from taking slices of a “double-napped” cone.

– OR “A section or a slice through A cone.”

– OR A conic section is a figure formed by the intersection of a plane and a circular cone. Depending on the angle of the plane with respect to the cone.

Types Of conic Sections• Parabola• Ellipse• Circle• Hyperbola

Hyperbola

Parabola

Ellipse

Circle

A little history:Conic sections date back to Ancient

Greece and was thought to discovered by Menaechmus around 360-350 B.C. What eventually resulted in the discovery of conic sections began with a simple problem.

It is believed that the great king Minos wanted to build a Tomb of his son, Glaucus, but felt that his tomb was too small. This was later deemed “Doubling the cube”.

Menaechmus was at that time and a student of Eudoxus, a famous Greek scholar. To solve the case of “doubling the cube” he focused on mean proportions and

the use of construction of a cone. Eventually his solution became known as “Conic sections”.

World Applications• Conic sections are used by

architects and architectural engineers. They can be seen in wide variety in the world in buildings, churches, and arches.

Parabola:• A set of all the points in the plane

equidistant from a given fixed point and a given fixed line in the

plane is a parabola.– The fixed point is focus.

– The fixed line is the directrix.

Applications of Parabolao Parabolas are everywhere in modern society. Parabolas can be found

in most things we encounter everyday. parabolas are formed when a football is kicked, a baseball is hit, a basketball hoop is made, dolphins jump and much more. The bottom of Eiffel Tower is a Parabola and it can be interpreted

as a negative parabola as it opens down. Parabola is the path of any object thrown in the air and is the

mathematical curve used by engineers in designing some suspension bridges. The properties of parabola make it the ideal shape for reflector of an automobile headlight.

• Parabola was used back in the medieval period with the use of cannons and cannon balls. Armies used parabolas to navigate the path of a cannon ball to attack the enemy.

• The swing set are like parabolas because of their U shape.• The ST. louis was designed in the shape of parabola.• Gallilo was the first person to show tha the path of an object thrown in the

space is a parabola

• Two Parabolas connect to make the Mcdonald’s M.• It is also used when making roller coasters because the points that

connect the roller coaster are the same distance away from the focus, it is able to create a parabola that is concave down.

Ellipse:• An ellipse is the set of all points in the plane, the sum of whose

distances from two fixed points is a given positive constant that is greater than the distance between the fixed points.

Application of Ellipse:• Ellipse are contributed to the real world

because of Oval shape.• Tilt a glass of water and the surface of the

liquid acquires an elliptical outline.• The Tycho Brahe plantarium is located in

Denmark.this building takes the form of an ellipse and it is clearly shown. Any cylinder sliced at an angle will reveal an ellipse.

• Footballs are elliptic.

• Your eye is an ellipse! It is a horizontal ellipse, the eye ball can be considered the center and the surrounding shape forms an ellipse, the minor axis is vertical and the major axis is horizontal across the eye. The two ends of the eye can be considered as vertex.

• Bicycle chain is an example of ellipse.• Earth orbit around the sun is an ellipse. Without the orbit we all .

• The ellipse is found in the rotation of planets in solar system. All planets orbit around the sun creates an ellipse.

Circle:• Definition:

A round plane figure whose boundary (the circumference) consists of points equidistant from a fixed point (the centre).

Applications of circles:• Most, if not all,

clocks are circular.• Ferris wheels are

circular.• Mostly Pizza’s are

circle.• Conic sections are

every where shown by water ripples from these rain drops.

• Gears and records along with CD’s are ideal examples of circles in real life. They are, and were in their time, essential to every day life.

• Bangles and Rings are examples of circle• Circles are used in real life situation as

wheels on cars bikes and other forms of transportation. The shape of a circle helps create a smooth movement for a car or a bike to move from place to place.

• Doughnut is a perfect example of a circle. The shape is prime factorization of the delicacy. It allows a baker to induce a heat distribution to create an evenly backed delicious doughnut.

Hyperbola:• Definition:

A hyperbola is the set of all points in the plane, the difference of whose distances from two fixed distinct points is given a positive constant that is less than the distance between them.

Applications of Hyperbola• In the architecture of the James S Mcdonell

planetarium, a hyperbola is formed.• When you turn a lamp on, you get a

hyperbola, if the the lamp is open from the top and the bottom the light comes out and form a hyperbola. The asymptote can be seen coming out from top and the bottom.

• In Nuclear cooling towers the hyperbolic shape is used due to its due to its ability to withstand high winds, while also making it in the most efficient was possible.

• A glass lens uses light contraction to magnify objects. Light is reflected in and out of the lens in a hyperbolic way creating a zoom.

• Radio waves and hyperbolas can be used in navigation.

If the centre of each circle gives out a radio signal then the signals will intersect each other in hyperbolas.

This is how hyperbolic radio navigation systems were created.

A sonic boom shock wave has the shape of a cone, and it intersects the ground in part of a hyperbola. It hits every point on this curve at the same time, so that people in different places along the curve on the ground hear it at the same time. Because the

airplane is moving forward, the hyperbolic curve moves forward and eventually the boom can be heard by everyone in its path.