this talks about the real life applications of conic sections namely circle, parabola, hyperbola and ellipse. art integrated project for class 11 maths - CBSE

1. Conic Sections in Daily
Life
-Aarush Pruthi, Aditya Garg, Aditya Bhatnagar,
Alay Singh Negi, Anagh Goyal,

2. Index
 Parabola in real life
 Ellipse in real life
 Hyperbola in real life
 Circles in real life

3. Parabola: Definition
 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 equation of a parabola is;
ax2+bx+c=0
 The fixed point is focus.
 The fixed line is the directrix

4. Parabola in everyday life
 The satellite dish is a parabolic
structure facilitating focus and
reflection of radio waves
 Water from a fountain takes a path
of parabola to fall on the earth.
The Golden Gate Bridge in San
Francisco in California is famous with
parabolic spans on both sides.
A ball thrown high follows the path
of a parabola

5.  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.

6. Ellipse: Definition
 The major axis is the longest
diameter of the ellipse (usually
denoted by ‘a’) going through the
centre from one end to the other, at
the broad part of the ellipse. the
minor axis is the shortest diameter of
ellipse (denoted by ‘b’), crossing
through the centre at the narrowest
part.
 The equation of the ellipse is given
by;
x2/a2 + y2/b2 = 1

7. Ellipse in everyday life
 Electrons in the atom move around the nucleus in an elliptical path of orbit.
 Paul’s Cathedral is an elliptical shaped structure to facilitate talking at one end is
heard at the other end using the property of ellipse.
 Food items carrot, cucumber cut at an angle to its main axis results in elliptical shape
and elegant look.

8.  The ellipse is found in the rotation of planets in solar system. All planets orbit
around the sun creates an ellipse.
 Footballs are elliptic.
 Your eye is an ellipse!

9. Hyperbola: Definition
 A hyperbola is the locus of all those points in a plane
such that the difference in their distances from two
fixed points in the plane is a constant.
 the equation with centre at origin and transverse axis
along the x-axis is:
 similarly, equation with centre at origin and conjugate
axis along the y-axis is:
 The line segment passing through both foci is the
transverse axis of the hyperbola. The line segment
perpendicular to the transverse axis and passing
through the centre represents the conjugate axis of
the hyperbola.‘2a’ denotes the length of the
transverse axis. ‘2b’ is the length of the conjugate
axis. ‘2c’ represents the distance between the two
foci.

10. Hyperbola in everyday life
 Lens, monitors, and optical glasses are of hyperbola shape.
 Hyperbolas are used in a navigation system known as LORAN (long range
navigation)
 The huge chimney of a nuclear power plant has the shape of a hyperbola, as
does the architecture of the James S. McDonnell Planetarium of the St. Louis
Science Center

11.  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.

12. Circles: Definition
 A circle is a set of all points which are equally spaced
from a fixed point in a plane. The fixed point is called the
centre of the circle. The distance between the centre and
any point on the circumference is called the radius of the
circle.
 The equation of a circle, with the centre as the origin is,
x2 +y2= r2
 Where “r” is the radius of the circle.
 The equation of the circle with centre (h, k)and the
radius ‘r’ is,
(x-h)2+(y-k)2 = r2
 which is called the standard form for the equation of a
circle.

13. Circle in everyday life
 Ferris wheels are circular.
 Mostly Pizza’s are circle.
 Bangles and Rings are examples of circle.
 Donuts are circular. It allows a baker to induce an equal heat
distribution.

14.  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.
 Gears and records along with CD’s are ideal examples.
 A circle is formed by rain drops by water ripples.

15. Bibliography
 https://www2.slideshare.net/slayerix/conic-section?qid=5d4cdcf6-c397-4a5f-
ae0c-dcf871b5762c&v=&b=&from_search=2
 http://mathcentral.uregina.ca/QQ/database/QQ.09.02/william1.html
 https://www.cuemath.com/learn/mathematics/conics-in-real-life/
 https://www2.slideshare.net/iramkhan66/applications-of-conic-sections3

16. THANK YOU