Grade 11 Math: Ellipses
This worksheet covers key concepts of ellipses, including their equations, foci, vertices, and graphing.
Includes
Standards
Topics
Ellipses: Equations and Properties
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Read each question carefully and provide the best answer. Show all your work for full credit.
1. What is the standard form equation of an ellipse centered at the origin with a horizontal major axis?
x²/a² + y²/b² = 1
x²/b² + y²/a² = 1
(x-h)²/a² + (y-k)²/b² = 1
(x-h)²/b² + (y-k)²/a² = 1
2. For an ellipse, the sum of the distances from any point on the ellipse to the two foci is equal to:
2c
2a
2b
a + b
3. The of an ellipse is the longest diameter, passing through both foci and vertices.
4. The distance from the center to each focus is denoted by .
5. Consider the ellipse with the equation (x²/25) + (y²/9) = 1. Identify the lengths of the major and minor axes, the coordinates of the vertices, and the coordinates of the foci.
6. An ellipse is a set of all points in a plane such that the sum of the distances from two fixed points (foci) is constant.
True
False
7. Graph the ellipse given by the equation x²/16 + y²/4 = 1. Label the vertices and foci.
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