Ellipses. Learning to Graph The Equation, and Finding the Equation From The Graph.

What is the meaning of the ellipse formula? What are the foci? What is the difference between the major, and minor axis? ... How may I graph an ellipse if I have the standard equation? How this may be done if the equation is not in standard form? How do I determine if the ellipse is horizontal or vertical? I have forgotten to complete the square, and to factor perfect square trinomials!

The aim of this lesson is to present the ellipse showing each one of the involved steps; including how you have to complete the square, and how you need to factor perfect square trinomials. You will view problems that go from the equation to the graph, and vice versa. Struggling students find it very friendly and constructive, advanced students find it challenging interesting!

Lesson's Content

Lesson's Glossary

Axis of Symmetry: A line on which a graph is reflected onto itself.

Center of the ellipse: The point where the major and minor perpendicular axis intersect.

Completing the Square: Method that finds the constant term in an incomplete perfect square trinomial of a second degree equation to solve it.

Conic section: A figure that is obtained slicing a double cone with a plane. (parabola, circle, hyperbola, and ellipse)

Ellipse All the points in a plane for which the distance to the foci (each focus) is constant.

Factoring: The process to brake a polynomial down into the product of several factors.

Factors: All whole numbers that are multiplied together to yield another number.

Factored Form: Any polynomial that is written as the product of polynomials of lower degree that may be obtained from the original polynomial.

Focus of an ellipse: Each one of the points in the major axis of the ellipse, from which sum of the distance from each to the set of points in the ellipse is constant.

Foci: Plural for focus.

Major axis: The major of the two perpendicular axis of symmetry in an ellipse, and in which are located the foci.

Minor axis: The smallest of the two perpendicular axis of symmetry in an ellipse.

Interactive Algebraic Applets

An ellipse is the space located around two points called foci, for which the

sum of the distances from each one of them to a point in this space is

constant. This interactive algebraic applet will show you this relationship.

You will be able to drag the point around the ellipse, and view how

the sum of these distances remain constant.

Ellipses may be horizontal or vertical. All depends in the values of the

parameters a, and b in the formula. They may be translated around the

coordinate plane by changing the values for the center (h,k).

This interactive algebraic applet presents the opportunity to drag the

sliders associated with each one of these parameters to view; how

the ellipse changes from horizontal to vertical, and how is translated.

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