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Conic Sections




 
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More Lessons for Intermediate Algebra or Algebra II

Math Worksheets

A series of free, online Intermediate Algebra Lessons or Algebra II lessons.
Videos, worksheets, and activities to help Algebra students.

In this lesson, we will learn

  • about conic sections
  • how to graph the equation of a parabola given in standard form and general form
  • how to graph the equation of a circle given in standard form and general form
  • how to graph the equation of an ellipse given in standard form and general form


Introduction to Conic Sections

By definition, a conic section is a curve obtained by intersecting a cone with a plane. In Algebra II, we work with four main types of conic sections: circles, parabolas, ellipses and hyperbolas. Each of these conic sections has different characteristics and formulas that help us solve various types of problems.

This video shows how you can generate a circle, ellipse, parabola, and hyperbola by intersecting a cone with a plan. It is the first of several videos on the conic sections.

This video introduces the idea of what a conic section is.



Conic Section: Parabola

Conic Sections: The Parabola part 1 of 2
This video defines a parabola and explains how to graph a parabola in standard form.
Conic Sections: The Parabola part 2 of 2
This video explains how to graph a parabola given in general form by rewriting it in standard form.


 

Conic Section: Circle

When working with circle conic sections, we can derive the equation of a circle by using coordinates and the distance formula. The equation of a circle is (x - h)2 + (y - k)2 = r2 where r is equal to the radius, and the coordinates (x,y) are equal to the circle center. The variables h and k represent horizontal or vertical shifts in the circle graph.

This video explains how to graph a circle in standard form and general form.

Conic Sections: Introduction to Circles


Conic Section: Ellipse

An ellipse is an important conic section and is formed by intersecting a cone with a plane that does not go through the vertex of a cone. The ellipse is defined by two points, each called a focus. From any point on the ellipse, the sum of the distances to the focus points is constant. The position of the foci determine the shape of the ellipse. The ellipse is related to the other conic sections and a circle is actually a special case of an ellipse.

How to talk about an ellipse.

Conic Sections: The Ellipse part 1 of 2
This video defines an ellipse and explains how to graph an ellipse in standard form.
Conic Sections: The Ellipse part 2 of 2
This video explains how to graph an ellipse in general form.


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