Introduction to Conic Sections

This course introduces the conic section and its different types, namely circle, parabola, ellipse. It starts with an introduction to the parabola and its standard equation. This section also covers how to find the axis, directrix, vertex, focus, length, and equation of the latus rectum. The second section introduces the overview of the circle, equation of a circle, center, radius and the properties of circle. The next section includes the ellipse and its standard equation. It explains how to determine the equation and length of the major and minor axis, center, directrix and length, and equation of the latus rectum.

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337 lectures

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Course Curriculum

40 videos

Powers and Polynomial

25 videos

Rational Numbers

11 videos

41 videos

Exponential Functions

15 videos

61 videos

Parametric Equations

5 videos

Introduction to Vectors

15 videos

15 videos

Polar Coordinates

5 videos

30 videos

Introduction to Conic Sections

23 videos

15 videos

Introduction to Combinatorics and Probability

16 videos

Introduction to Sequences and Series

20 videos

Introduction to Conic Sections Lectures

Introduction to Conic Sections

Three Forms Of Parabolas - Example 4

In mathematics, a parabola is a two-dimensional, mirror-symmetrical curve, which is approximately U-shaped when oriented, but which can be in any orientation in its plane. The parabola has many important applications, from an antenna (parabolic antenna) to a ballistic parabola.

Lily An

Introduction to Conic Sections

Applications Of Parabolas - Example 1

In mathematics, a parabola is a curve that is in the form of U-shaped approximately. In parabola, the focus is the point where the curve of the parabola is closest to the "x"-axis, the directrix is the line containing the focus and perpendicular to the axis of symmetry of the parabola and the latus rectum is the chord of the parabola which passes through the focus and is parallel to the directrix.

Lily An

Introduction to Conic Sections

Applications Of Parabolas - Example 2

In mathematics, a parabola is a curve that is in the form of U-shaped approximately. In parabola, the focus is the point where the curve of the parabola is closest to the "x"-axis, the directrix is the line containing the focus and perpendicular to the axis of symmetry of the parabola and the latus rectum is the chord of the parabola which passes through the focus and is parallel to the directrix.

Lily An

Introduction to Conic Sections

Applications Of Parabolas - Example 3

In mathematics, a parabola is a curve that is in the form of U-shaped approximately. In parabola, the focus is the point where the curve of the parabola is closest to the "x"-axis, the directrix is the line containing the focus and perpendicular to the axis of symmetry of the parabola and the latus rectum is the chord of the parabola which passes through the focus and is parallel to the directrix.

Lily An

Introduction to Conic Sections

Applications Of Parabolas - Example 4

In mathematics, a parabola is a curve that is in the form of U-shaped approximately. In parabola, the focus is the point where the curve of the parabola is closest to the "x"-axis, the directrix is the line containing the focus and perpendicular to the axis of symmetry of the parabola and the latus rectum is the chord of the parabola which passes through the focus and is parallel to the directrix.

Lily An

Introduction to Conic Sections

Circles - Overview

In mathematics, the circle is a simple closed curve in Euclidean space. The distance between any of the points and the centre is called the radius. The point opposite to the centre is called the centre. The diameter is the length of the line segment between the centre and the perimeter. Circles may also be subdivided into arc segments.

Lily An

Introduction to Conic Sections

Circles - Example 1

In mathematics, the circle is a simple closed curve in Euclidean space. The distance between any of the points and the centre is called the radius. The point opposite to the centre is called the centre. The diameter is the length of the line segment between the centre and the perimeter. Circles may also be subdivided into arc segments.

Lily An

Introduction to Conic Sections

Circles - Example 2

In mathematics, the circle is a simple closed curve in Euclidean space. The distance between any of the points and the centre is called the radius. The point opposite to the centre is called the centre. The diameter is the length of the line segment between the centre and the perimeter. Circles may also be subdivided into arc segments.

Lily An

Introduction to Conic Sections

Circles - Example 3

In mathematics, the circle is a simple closed curve in Euclidean space. The distance between any of the points and the centre is called the radius. The point opposite to the centre is called the centre. The diameter is the length of the line segment between the centre and the perimeter. Circles may also be subdivided into arc segments.

Lily An

Introduction to Conic Sections

Circles - Example 4

In mathematics, the circle is a simple closed curve in Euclidean space. The distance between any of the points and the centre is called the radius. The point opposite to the centre is called the centre. The diameter is the length of the line segment between the centre and the perimeter. Circles may also be subdivided into arc segments.

Lily An

Introduction to Conic Sections

Circles - Example 5

In mathematics, the circle is a simple closed curve in Euclidean space. The distance between any of the points and the centre is called the radius. The point opposite to the centre is called the centre. The diameter is the length of the line segment between the centre and the perimeter. Circles may also be subdivided into arc segments.

Lily An

Introduction to Conic Sections

Circles - Example 6

In mathematics, the circle is a simple closed curve in Euclidean space. The distance between any of the points and the centre is called the radius. The point opposite to the centre is called the centre. The diameter is the length of the line segment between the centre and the perimeter. Circles may also be subdivided into arc segments.

Lily An

Introduction to Conic Sections

Circles - Example 7

In mathematics, the circle is a simple closed curve in Euclidean space. The distance between any of the points and the centre is called the radius. The point opposite to the centre is called the centre. The diameter is the length of the line segment between the centre and the perimeter. Circles may also be subdivided into arc segments.

Lily An

Introduction to Conic Sections

Circles - Example 8

In mathematics, the circle is a simple closed curve in Euclidean space. The distance between any of the points and the centre is called the radius. The point opposite to the centre is called the centre. The diameter is the length of the line segment between the centre and the perimeter. Circles may also be subdivided into arc segments.

Lily An

Introduction to Conic Sections

Ellipses - Overview

In mathematics, an ellipse is a curve in a plane surrounding two focal points such that the sum of the distances to the two focal points is constant for every point on the curve. The two focal points (also called the foci) are the endpoints of the major axis of the ellipse. The length of the major axis is called the "semimajor axis" of the ellipse, and the distance between the two focal points is called the "semiminor axis". The shape of an ellipse is represented by its eccentricity, which for an ellipse can be any number from 0 (a circle) to arbitrarily close to, but not equal to, 1 (a line). The eccentricity of an ellipse is the ratio of the distance between the foci to the length of the semimajor axis. A circle has an eccentricity of exactly one, and an ellipse can have an eccentricity that is any real number greater than zero.

Lily An

Introduction to Conic Sections

Ellipses - Example 1

In mathematics, an ellipse is a curve in a plane surrounding two focal points such that the sum of the distances to the two focal points is constant for every point on the curve. The two focal points (also called the foci) are the endpoints of the major axis of the ellipse. The length of the major axis is called the "semimajor axis" of the ellipse, and the distance between the two focal points is called the "semiminor axis". The shape of an ellipse is represented by its eccentricity, which for an ellipse can be any number from 0 (a circle) to arbitrarily close to, but not equal to, 1 (a line). The eccentricity of an ellipse is the ratio of the distance between the foci to the length of the semimajor axis. A circle has an eccentricity of exactly one, and an ellipse can have an eccentricity that is any real number greater than zero.

Lily An

Introduction to Conic Sections

Ellipses - Example 2

In mathematics, an ellipse is a curve in a plane surrounding two focal points such that the sum of the distances to the two focal points is constant for every point on the curve. The two focal points (also called the foci) are the endpoints of the major axis of the ellipse. The length of the major axis is called the "semimajor axis" of the ellipse, and the distance between the two focal points is called the "semiminor axis". The shape of an ellipse is represented by its eccentricity, which for an ellipse can be any number from 0 (a circle) to arbitrarily close to, but not equal to, 1 (a line). The eccentricity of an ellipse is the ratio of the distance between the foci to the length of the semimajor axis. A circle has an eccentricity of exactly one, and an ellipse can have an eccentricity that is any real number greater than zero.

Lily An

Introduction to Conic Sections

Ellipses - Example 3

In mathematics, an ellipse is a curve in a plane surrounding two focal points such that the sum of the distances to the two focal points is constant for every point on the curve. The two focal points (also called the foci) are the endpoints of the major axis of the ellipse. The length of the major axis is called the "semimajor axis" of the ellipse, and the distance between the two focal points is called the "semiminor axis". The shape of an ellipse is represented by its eccentricity, which for an ellipse can be any number from 0 (a circle) to arbitrarily close to, but not equal to, 1 (a line). The eccentricity of an ellipse is the ratio of the distance between the foci to the length of the semimajor axis. A circle has an eccentricity of exactly one, and an ellipse can have an eccentricity that is any real number greater than zero.

Lily An

Introduction to Conic Sections

Ellipses - Example 4

In mathematics, an ellipse is a curve in a plane surrounding two focal points such that the sum of the distances to the two focal points is constant for every point on the curve. The two focal points (also called the foci) are the endpoints of the major axis of the ellipse. The length of the major axis is called the "semimajor axis" of the ellipse, and the distance between the two focal points is called the "semiminor axis". The shape of an ellipse is represented by its eccentricity, which for an ellipse can be any number from 0 (a circle) to arbitrarily close to, but not equal to, 1 (a line). The eccentricity of an ellipse is the ratio of the distance between the foci to the length of the semimajor axis. A circle has an eccentricity of exactly one, and an ellipse can have an eccentricity that is any real number greater than zero.

Lily An

Introduction to Conic Sections

Three Forms of a Parabola - Overview

In mathematics, a parabola is a curve in a plane that is defined by a quadratic function, y = x (a = 0). A parabola is a conic section (a plane curve resulting from the intersection of a cone with a plane parallel to an element of the cone).

Lily An

Introduction to Conic Sections

Three Forms of a Parabola - Example 1

In mathematics, a parabola is a curve in a plane that is defined by a quadratic function, y = x (a = 0). A parabola is a conic section (a plane curve resulting from the intersection of a cone with a plane parallel to an element of the cone).

Lily An

Introduction to Conic Sections

Three Forms of a Parabola - Example 2

In mathematics, a parabola is a curve in a plane that is defined by a quadratic function, y = x (a = 0). A parabola is a conic section (a plane curve resulting from the intersection of a cone with a plane parallel to an element of the cone).

Lily An

Introduction to Conic Sections

Three Forms of a Parabola - Example 3

In mathematics, a parabola is a curve in a plane that is defined by a quadratic function, y = x (a = 0). A parabola is a conic section (a plane curve resulting from the intersection of a cone with a plane parallel to an element of the cone).

Lily An