Parabola, hyperbola and its applications

PPT on Parabola, hyperbola and its applications made by the students of SVIT,Vasad under the subject Engineering graphics.

1. Introduction to different methods to draw parabola and hyperbola and its applications Engineering graphics FY CE 1 Batch B Name Enrollment no Aarti 170410107 014 Priyanka 170410107 019 Dhananjaysinh 170410107 027 Hiral 170410107 059 Avani 170410107 099 Aarsh 170410107 115

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 r ectangular 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.

5. 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.

6. 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

7. 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.

8. 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 .

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

10. 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 .

11. 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.

12. Focus vertices method Draw hyperbola with e=8/5, where vertex V is at a dist. of 25 mm from directrix.

13. 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.

14. Drawing a rectangular hyperbola A point P is 20 mm and 30mm respectively from two straight lines at 90 o to each other, draw rectangular hyperbola from P within 6 mm distance from each line.

15. 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 .

16. Water tanks: Shape of overhead water tanks is hyperbolic.

17. 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