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 definition
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 .
Ellipse Equation
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?
Horizontal Ellipse
Horizontal Ellipse happens when . Where are the foci and vertices located?
Vertical Ellipse
Vertical Ellipse happens when . What is the length of major axis of such ellipse?
Vertical Ellipse
Vertical Ellipse happens when . Where are the foci and vertices located?
Exercise
Ellipse orientation
Is the ellipse horizontal or vertical?
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?
The value of a, b, and c
Write the value of a, b, and c.
Equation
Write the equation of the ellipse.