Eccentricity of Conic Sections
Explore the concept of eccentricity as it applies to different conic sections, including circles, ellipses, parabolas, and hyperbolas.
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Eccentricity of Conic Sections
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Read each question carefully and provide the best answer based on your understanding of eccentricity in conic sections. Show all your work where applicable.
1. Which of the following conic sections has an eccentricity (e) equal to 0?
Ellipse
Parabola
Circle
Hyperbola
2. An ellipse has an eccentricity (e) such that:
e = 1
e < 1
e > 1
e = 0
3. The eccentricity of a parabola is always equal to .
4. A hyperbola has an eccentricity (e) that is always than 1.
5. The eccentricity of a conic section describes how much it deviates from a perfect circle.
True
False
6. An ellipse has a semi-major axis of length 'a' and a distance from the center to a focus of 'c'. Write the formula for its eccentricity.
7. What happens to the shape of an ellipse as its eccentricity approaches 0?
8. Observe the ellipse below. If the distance from the center to a focus is 3 units and the length of the semi-major axis is 5 units, calculate the eccentricity.
Match each conic section to its characteristic eccentricity value.
9. Circle
a. e > 1
10. Parabola
b. e = 0
11. Ellipse
c. 0 < e < 1
12. Hyperbola
d. e = 1