# 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.