The document introduces various methods for drawing parabolas and hyperbolas, including techniques such as the rectangle method, directrix-focus method, and tangent/triangle method. It discusses the applications of these conic sections in fields like engineering graphics, mentioning specific uses like bridge arches, light reflectors, and gas law representations. Additionally, it covers hyperbolas, their characteristics, and applications, highlighting their relevance in structures like water tanks and cooling towers.

1. INTRODUCTION TO DIFFERENT
METHODS TO DRAW PARABOLA
AND HYPERBOLA AND ITS
APPLICATIONS
Engineering graphics
FY CE 1 Batch B
Name Enrollment no
Aarti 170410107014
Priyanka 170410107019
Dhananjaysinh 170410107027
Hiral 170410107059
Avani 170410107099
Aarsh 170410107115

2. INDEX
 What is parabola ?
 Rectangle method for parabola
 Directrix focus method for parabola
 Tangent/triangle method for parabola
 Applications of parabola
 What is hyperbola ?
 Directrix focus method for hyperbola
 Focus vertices method for hyperbola
 What is rectangular hyperbola ?
 Drawing a rectangular hyperbola
 Applications of hyperbola

3. WHAT IS PARABOLA ?
 When the section plane is inclined to the axis and
parallel to one of the generators of the cone, the
section obtained is called a parabola.

4. RECTANGLE METHOD FOR PARABOLA
 E.g. draw a parabola with axis height 50 mm, and
base length 80mm by rectangle method.

6. DIRECTRIX FOCUS METHOD FOR PARABOLA
 E.g. construct a parabola when distance of focus
from the directrix is 50 mm and draw a tangent and
normal at a point on it 40 mm from F.

8. TANGENTS/TRIANGLE METHOD FOR PARABOLA
 E.g. draw a parabola with axis height 50 mm, and
base length 80mm by triangle method.
 Steps:
 Draw the base AB and axis OM, such that OM is
perpendicular bisector to AB.
 Mark P on line OM such that OM=MP.
 join P,A and P, B. these are the tangents to the parabola
at A and B.
 Divide AP and BEP in to the same number of the equal
parts(10 here)
 join 1,1 ; 2,2 ; 3,3; etc.... From PA to PB.
 A smooth curve passing through A,M and B tangential to
the above lines is the required parabola

10. APPLICATIONS OF PARABOLA
 Arches of bridges:
 An arch bridge is a bridge with abutments at each end
shaped as a curved arch.
 Abutments are the substructures at the ends of a
bridge.

11.  Light reflectors:
 Reflectors for the parallel beams used in the head
lamps of a vehicle are parabolic in shape.
 Sound reflectors and detectors are also parabolic in
shape.

12.  Different paths such as projected missiles or any
object thrown up at any angle from earth follows a
parabolic path.

14. WHAT IS HYPERBOLA ?
 When the section plane is inclined to the axis of the
cone such that the angle made by the section plane
with axis is smaller than the angle made by the
generator of the cone with the axis, the section
obtained is called hyperbola.

15. DIRECTRIX FOCUS METHOD FOR HYPERBOLA
 Draw a hyperbola when dist. of focus from directrix
is 45 mm and point moves such that e=5/4.

17. FOCUS VERTICES METHOD
 Draw
hyperbola
with e=8/5,
where vertex
V is at a dist.
of 25 mm
from
directrix.

18. WHAT IS RECTANGULAR HYPERBOLA ?
 It is the curve traced by a point moving in a plane
such that the product of its distances from the
asymptotes at right angle to each other is constant.

19. DRAWING A RECTANGULAR HYPERBOLA
 A point P is 20 mm and 30mm respectively from two
straight lines at 90o to each other, draw rectangular
hyperbola from P within 6 mm distance from each
line.

21. APPLICATIONS OF HYPERBOLA
 Nature of boyle’s law graph
 For a fixed amount of an ideal gas kept at a fixed
temperature, pressure and volume are inversely
proportional. Or Boyle's law is a gas law, stating
that the pressure and volume of a gas have an
inverse relationship, when temperature is held
constant.

22.  Water tanks:
 Shape of overhead water tanks is hyperbolic.

23.  Cooling towers:
 A cooling tower is a heat rejection device that
rejects waste heat to the atmosphere through the
cooling of a water stream to a lower temperature.
Cooling towers may either use the evaporation of
water to remove process heat and cool the working
fluid. They are seen in power plants