Conics Group Members Talha Zameer Zeeshan Shabbir Fiaz Ashraf M.Bilal Hammad Hassan Umair Ali

Conic Sections There are four conics in the conics sections Parabolas Circles Ellipses and Hyperbolas. We see then everyday but we just don’t notice them. They appear everywhere in the world and can be man-made or natural. The applications of conics can be seen everyday all around us. Conics are found in architecture, physics, astronomy and navigation. If you get lost, you can use a GPS and it will tell where you are (a point) and it will lead you to your destination (another point). Conics are also used to describe the orbits of planets, moons and satellites in our universe.

Conic Sections A conic section (or just conic) is a curve obtained as the intersection of a cone with a plane.

Parts of Conic Section CIRCLE ELLIPSE PARABOLA HYPERBOLA

Introduction Fiaz Ashraf

Introduction The conic sections were first identified by Menaechus in about 350 BC, but he used three different types of cone, taking the same section in each, to produce the three conic sections, ellipse, parabola and hyperbola. It was Apollonius of Perga, (c. 255–170 BC) who gave us the conic sections using just one cone. Evidence of wheeled vehicles appears from the second half of the 4th millennium BC. The first wheeled vehicle was invented in 3500-3350 BC. 1700 BC – The Rhind Papyrus gives a method to find the area of a circular field. The first theorems relating to circles are attributed to Thales around 650 BC 300 BC – Book III of Euclid’s Element deals with the properties of circles. If we cut a cone at different angles, then we will obtain different types of conic section. There are four different types we can obtain.

The circle, where the cone is cut at right-angles to its axis.

The ellipse, where the cone is cut at an oblique angle shallower than a generator.

The parabola, where the cone is cut parallel to a generator.

The hyperbola, where a double cone is cut at an angle steeper than a generator.

Circle Zeeshan Shabbir

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

Properties of Circle All Circles are symmetrical. All circles do not have edges. All circles are proportionate. All line segments starting from the middle of the circle to the circumference is equal.

Real Life Applications Circle play a really large role in our life. We just fail to realize it even through it is right in front of us. Things that we commonly use are round. Earth, Car tires, Coins, Man Holes, etc.

Real Life Application Wheels & Gears Wheel is one of the greatest invention of all time and the basis of much of our transportation system. Circular gears are important elements in many of the machines we use every day, from CD players to electric saws.

Real Life Application Ferris Wheel One prime example of a circle that you can find in real life is a Ferris Wheel.  All the points along the outer rim of the wheel are equidistant from the center.

Ellipse Hammad Hassan

Ellipse A regular oval shape, traced by a point moving in a plane so that the sum of its distances from two other points is constant, or resulting when a cone is cut by an oblique plane which does not intersect the base

Real Life Application If you tilt a glass of water, the resulting shape of the surface of the water is also an ellipse.

Real Life Applications Satellite and Planet Orbits Kepler's first law of planetary motion is: The path of each planet is an ellipse with the sun at one focus. 

Real Life Applications Football  If an ellipse is rotated about the major axis, you obtain a football.

Parabola M. Bilal

Parabola A symmetrical open plane curve formed by the intersection of a cone with a plane parallel to its side. The path of a projectile under the influence of gravity follows a curve of this shape.

Real Life Applications. Heaters Heaters are sold which make use of the relection property of the parabola.  The heat source is at the focus and heat is concentrated in parallel rays.

Real Life Applications. Fountains Fountains at Las Vegas exhibit water in the shapes of parabolas.

Real Life Applications. Path of Football The path of an object thrown in space is a parabola. 

Hyperbola Umair Ali

Hyperbola A symmetrical open curve formed by the intersection of a circular cone with a plane at a smaller angle with its axis than the side of the cone.

Real Life Applications House Lamp The shadow of a lampshade or a flashlight.

Real Life Applications Nuclear Reactors Cooling towers of Nuclear Reactors.

Real Life Applications Shapes Most potato chips are hyperbolic-paraboloids.

Thankxxx. . . . …