Mensuration - Cone, Circle, Ellipse, Parabola and Hyperbola

In mensuration we shall study about some other curves, viz., circles, ellipses, parabolas and hyperbolas. The names parabola and hyperbola are given by Apollonius. These curves are in fact, known as conic sections or more commonly conics because they can be obtained as intersections of a plane with a double napped right circular cone. These curves have a very wide range of applications in fields such as planetary motion, design of telescopes and antennas, reflectors in flashlights and automobile headlights, etc. Now, in the subsequent sections we will see how the intersection of a plane with a double napped right circular cone results in different types of curves.

Sections of a Cone

Let l be a fixed vertical line and m be another line intersecting it at a fixed point V and inclined to it at an angle α (Fig 11.1). Suppose we rotate the line m around the line l in such a way that the angle α remains constant. Then the surface generated is a double-napped right circular hollow cone herein after referred as cone and extending indefinitely far in both directions (Fig.11.2)

The point V is called the vertex; the line l is the axis of the cone. The rotating line m is called a generator of the cone. The vertex separates the cone into two parts called nappes. If we take the intersection of a plane with a cone, the section so obtained is called a conic section. Thus, conic sections are the curves obtained by intersecting a right circular cone by a plane.

We obtain different kinds of conic sections depending on the position of the intersecting plane with respect to the cone and by the angle made by it with the vertical axis of the cone. Let β be the angle made by the intersecting plane with the vertical axis of the cone (Fig11.3). The intersection of the plane with the cone can take place either at the vertex of the cone or at any other part of the nappe either below or above the vertex.

Introduction to Conic Sections

 

Latest Jobs

  1. Type
    Job Notification
    Job
    Indian Institute of Technology Hyderabad Recruitment of 152 JE, Engineer, Library Assistant, MTS - Last Date 17-02-2020
    Location
    HyderabadTelangana, India
    Date Posted
    6 Feb 2020
  2. Type
    Job Notification
    Job
    SBI Recruitment of 100 Specialist Officers - Last Date 12-02-2020
    Location
    Anywhere
    Date Posted
    4 Feb 2020
  3. Type
    Job Notification
    Job
    INDIAN Bank Recruitment 138 Specialist Officers - Last Date - 10-02-2020
    Location
    Anywhere
    Date Posted
    3 Feb 2020
  4. Type
    Job Notification
    Job
    KVIC Recruitment of 108 Group-B and Group-C categories - Last Date 19-01-2020
    Location
    MumbaiMaharashtra, India
    Date Posted
    7 Jan 2020
  5. Type
    Job Notification
    Job
    SAIL Durgapur Steel Plant Recruitment of Manager, Technician, Medical Service Provider - 27-01-2020
    Location
    DurgapurWest Bengal, India
    Date Posted
    7 Jan 2020
  6. Type
    Job Notification
    Job
    Indian Coast Guard Recruitment 260 Navik - Last Date 02-02-2020
    Location
    Anywhere
    Date Posted
    7 Jan 2020
  7. Type
    Job Notification
    Job
    IOCL hiring 312 Apprentices - Last Date 22-01-2020
    Location
    Anywhere
    Date Posted
    7 Jan 2020
  8. Type
    Job Notification
    Job
    RBI Recruitment NEWS for 926 Assistants - Last Date 16-01-2020
    Location
    Anywhere
    Date Posted
    7 Jan 2020
  9. Type
    Job Notification
    Job
    Janki Devi Memorial College Recruitment 71 Assistant Professor - Last Date 04-01-2020
    Location
    DelhiDelhi, India
    Date Posted
    2 Jan 2020
  10. Type
    Job Notification
    Job
    NPCIL Recruitment of Trainee, Electrician, Fitter, Machinist, Welder, Driver - Last Date 21-01-2020
    Location
    RawatbhataRajasthan, India
    Date Posted
    2 Jan 2020

Jobs by Category

Syllabus and Previous Papers

Leave a Reply

Your email address will not be published. Required fields are marked *