Ellipse (Graph and Equation)

Exploration of Definition

Drag point A to create the ellipse. Observe that the sum of AF1 and AF2 remains the same no matter to where A is located.

Ellipse Equation

You are going to explore the equation of ellipse with center at . There are four values you can change and explore.
• Center coordinate. Center in this app is written as . You can change the value of h and k by dragging the point in the grey sliders.
• The length of the horizontal segment from the center of the ellipse to a point in the ellipse. You can adjust the length using the red slider. This length is named .
• The length of the vertical segment from the center of the ellipse to a point in the ellipse. You can adjust the length using the blue slider. This length is named .

The Equation

An ellipse has center at (h,k) with is the distance between center and vertices. The distance between center and foci is and . What is the equation of the ellipse?

Horizontal Ellipse

Horizontal Ellipse happens when . What is the length of major axis of such ellipse?

Check all that apply

Horizontal Ellipse

Horizontal Ellipse happens when . Where are the foci and vertices located?

Check all that apply

Vertical Ellipse

Vertical Ellipse happens when . What is the length of major axis of such ellipse?

Check all that apply

Vertical Ellipse

Vertical Ellipse happens when . Where are the foci and vertices located?

Check all that apply

Ellipse orientation

Is the ellipse horizontal or vertical?

Check all that apply

Foci

Write the coordinates of the foci.

Center

Write the coordinate of the center

Vertices

Write the coordinates of the two vertices

Major and minor axis

What is the length of the major and minor axis respectively?

Check all that apply

The value of a, b, and c

Write the value of a, b, and c.

Equation

Write the equation of the ellipse.