Grade 11 · Math · Precalculus

11th grade How stretched is a conic? Eccentricity worksheet

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How stretched is a conic? Eccentricity

Grade 11 Math Worksheet - Challenge Me

NameDate

Circle the best answer, or write your answer on the line.

Ren writes the equation of an ellipse with a = 10 and e = 3/5. What is b², the other denominator?
Tala writes the equation of a hyperbola with a = 4 and e = 5/4. What is b², the other denominator?
Zee writes the equation of an ellipse with a = 13 and e = 12/13. What is b², the other denominator?
Jun writes the equation of a hyperbola with a = 8 and e = 17/8. What is b², the other denominator?
Mars comes within 206.7 million km of the Sun and goes out to 249.3 million km. Milo rounds e to the nearest hundredth. What is e?
Mercury comes within 46 million km of the Sun and goes out to 69.8 million km. Noah rounds e to the nearest hundredth. What is e?
7.
Pia compares three planets' orbits using the table shown. Which orbit is the most stretched?
- Earth
- Mercury
- Mars
8.
Ren compares three planets' orbits using the table shown. Which orbit is the most stretched?
- Neptune
- Mars
- Saturn
9.
Tala compares three planets' orbits using the table shown. Which orbit is the most stretched?
- Venus
- Mercury
- Jupiter
10.
Zee compares three planets' orbits using the table shown. Which orbit is the most stretched?
- Mars
- Uranus
- Venus

Eccentricity of ellipses and hyperbolas. Every version has 10 questions, and the answer key prints on the second page.

I can find e = c/a for an ellipse or a hyperbola from its distances or its equation.
I can name a conic from its eccentricity.
I can use e to find a missing denominator and to compare how stretched real orbits are.

Standard: G-GPE.A.3 (+)

eccentricity e: How stretched a conic is: c divided by a.

a: Distance from the center to a vertex (half the long axis).

c: Distance from the center to a focus.

focus (foci): A special point inside the curve; an ellipse has two.

orbit: The path a planet or comet takes around the Sun.

AU: Earth's average distance from the Sun, about 150 million km.

Divided the vertex distance by the focus distance, a/c, instead of c/a. Remind your child that e = c/a, the focus distance over the vertex distance.

Used the whole long axis instead of half of it for a.

Stopped at a squared value (c² or a²) instead of taking the square root.

Ask: is a measured from the center or from end to end?

Ask: is this c, or c squared?

What is the most common mistake with how stretched is a conic? eccentricity?

Divided the vertex distance by the focus distance, a/c, instead of c/a. Remind your child that e = c/a, the focus distance over the vertex distance.

Are these 11th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

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