Eccentricity of Conic Sections
This worksheet focuses on understanding and calculating the eccentricity of conic sections, including ellipses, hyperbolas, and parabolas, for Grade 11 students.
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Eccentricity of Conic Sections
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Read each question carefully and provide your answers in the space provided. Show all your work for full credit.
1. The eccentricity of an ellipse is always between and .
2. A parabola has an eccentricity equal to .
3. For a hyperbola, the eccentricity is always 1.
4. A circle is a special case of an ellipse with an eccentricity of .
5. Which of the following conic sections has an eccentricity of 0?
Parabola
Ellipse
Circle
Hyperbola
6. If the eccentricity of a conic section is 2.5, what type of conic section is it?
Ellipse
Parabola
Circle
Hyperbola
7. Define eccentricity in the context of conic sections.
8. An ellipse has a semi-major axis of length 5 and a focal length of 3. Calculate its eccentricity.
9. Consider an ellipse with the equation (x^2)/25 + (y^2)/16 = 1. Determine the eccentricity of this ellipse.
10. A hyperbola has a distance of 10 between its foci and a distance of 6 between its vertices. Calculate its eccentricity.
11. As the eccentricity of an ellipse approaches 1, the ellipse becomes more circular.
True
False
12. All parabolas have the same eccentricity.
True
False