Grade 12 Math: Ellipse Worksheet
This worksheet covers key concepts of ellipses, including their equations, foci, vertices, and eccentricity, suitable for Grade 12 Algebra students.
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Ellipse Worksheet
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Read each question carefully and provide your answers in the space provided. Show all your work for full credit.
1. Which of the following is the standard form equation of an ellipse centered at (h, k)?
(x-h)²/a² + (y-k)²/b² = 1
(x-h)²/a² - (y-k)²/b² = 1
(x-h)²/a² + (y-k)²/a² = 1
(x-h)²/b² + (y-k)²/a² = 0
2. What is the eccentricity of an ellipse?
The distance from the center to a vertex.
A measure of how 'stretched' the ellipse is.
The length of the minor axis.
The distance between the foci.
3. The two fixed points inside an ellipse are called the .
4. The longest diameter of an ellipse is called the axis.
5. Find the foci of the ellipse given by the equation (x²/25) + (y²/16) = 1.
6. Write the equation of an ellipse with foci at (±3, 0) and vertices at (±5, 0).
7. For an ellipse, the sum of the distances from any point on the ellipse to the two foci is constant.
True
False
8. An ellipse with an eccentricity of 0 is a circle.
True
False
9. Graph the ellipse given by the equation (x²/9) + (y²/4) = 1. Clearly mark the center, vertices, and co-vertices.
10. Consider the ellipse with the equation ((x-1)²/16) + ((y+2)²/9) = 1. Identify its center, vertices, co-vertices, and foci. Then, sketch the graph.
Center:
Vertices:
Co-vertices:
Foci: