Conic Sections Class 11

In Class 11, the study of conic sections is an important part of the mathematics curriculum, particularly in the field of coordinate geometry. Conic sections—circle, ellipse, parabola, and hyperbola—are significant because they provide a foundation for understanding various physical phenomena and have numerous practical applications in real life, such as in the paths of planets and satellites, optics, and engineering designs.

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Conic Sections

Conic Sections in Geometry: Conic Sections also called the section of the cone are the curves that are formed by the intersection of a plane and a cone. Thus, the name Conic Sections because they are the section of a cone. By the intersection of a cone with a plane, we formed four different types of conic sections namely,

  • Circle
  • Parabola
  • Hyperbola
  • Ellipse

In this article, we have covered What are Conic Section, Conic Section Formulas, Equations of Conic Sections, and others in detail.

Table of Content

  • What are Conic Sections?
    • Conic Sections Definition
  • Generated Conic Sections(Sections of Cone)
    • Conic Section Circle
    • Conic Section Ellipse
    • Conic Section Parabola
    • Conic Section Hyperbola
  • Focus, Eccentricity and Directrix of Conic Section
    • Focus
    • Directrix
    • Eccentricity
  • Conic Sections Parameters
  • Conic Section Formulas
  • Types of Conic Sections
    • Circle
    • Parabola
    • Hyperbola
    • Ellipse
  • Standard Form of Conic Sections
  • Conic Sections Equations
  • Conic Sections in Real Life
  • Conic Sections Examples
  • Conic Sections Class 11
  • Practice Questions on Conic Sections

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What are Conic Sections?

A Conic section, also referred to just as a ‘Conic’ is a plane intersecting a cone. Imagine a cone being cut by a knife at different places creating different types of curves, which are known as Conic Sections. The three main Conic sections Parabola, Hyperbola, and Ellipse (a Circle can be referred to as a type of ellipse)....

Generated Conic Sections(Sections of Cone)

Depending upon the different angles at which the plane is intersecting the Cone, different types of curves are found. Imagine that an ice cream cone is in the hands, looking at the cone from the top it look like a circle because the top view of an inverted cone is a circle, that gives a conclusion that cutting a cone with a plane exactly at 90° will provide a circle, Similarly, different angles will lead to different types of curves....

Focus, Eccentricity and Directrix of Conic Section

We define conic section as the locus of a point say (P) moving in the plane about a fixed point F (i.e. the Focus) and with respect to a fixed line known as Directrix (such that the focus point is never on d) and all of these are arranged such that the ratio of the distance of point P from focus F to the distance from d is always contact and the ratio is called the eccentricity(e)....

Conic Sections Parameters

Variou parameters of the conic section that are used to explain and trace various conic section are,...

Conic Section Formulas

Various Conic Section Formulas that are associated to the conic section are added in the table below,...

Types of Conic Sections

Intersectiong a plane with the cone we get different types of the conic sections. There are four general types of conic section that are,...

Standard Form of Conic Sections

The standard form of the conic section is added below, For ellipses and hyperbolas, the standard form has the x-axis as the principal axis and the origin (0,0) as the centre. The vertices are (±a, 0) and the foci (±c, 0). For the standard form the conic section always passes through the origin. The standard form of the various conic section are,...

Conic Sections Equations

The standard equations of the conic section are added in the table below,...

Conic Sections in Real Life

Various instances where we use the conic sections in our real life includes,...

Conic Sections Examples

Example 1: Find the equation of a circle that has a centre of (0,0) and a radius is 5....

Conic Sections Class 11

In Class 11, the study of conic sections is an important part of the mathematics curriculum, particularly in the field of coordinate geometry. Conic sections—circle, ellipse, parabola, and hyperbola—are significant because they provide a foundation for understanding various physical phenomena and have numerous practical applications in real life, such as in the paths of planets and satellites, optics, and engineering designs....

Practice Questions on Conic Sections

Q1: For a hyperbola with vertices (±2, 0) and foci at (±3, 0). Find the equation of the hyperbola....

Conic Sections – FAQs

What is Conic Section in Geometry?...