Eccentricity of Conic Sections
Grade 12 Math worksheet covering the eccentricity of ellipses, parabolas, and hyperbolas, including calculations and properties.
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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. What is the eccentricity of a parabola?
e < 1
e = 1
e > 1
e = 0
2. An ellipse has an eccentricity of 0.75. Which of the following statements is true?
It is a circle.
It is very elongated.
It is nearly circular.
It is a hyperbola.
3. The eccentricity of a circle is .
4. For a hyperbola, the eccentricity 'e' is always than 1.
5. The eccentricity of an ellipse determines its .
6. An ellipse has a semi-major axis of length 5 and a focal distance of 3. Calculate its eccentricity.
7. Describe the relationship between the eccentricity of an ellipse and its shape. Use a diagram to illustrate your answer.
8. A conic section with an eccentricity of 0 is a hyperbola.
True
False
9. As the eccentricity of an ellipse approaches 1, the ellipse becomes more elongated.
True
False
10. The equation of a conic section is given by 9x² + 4y² - 36x + 8y + 4 = 0. Determine the type of conic section and calculate its eccentricity.