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 - Building Confidence

NameDate

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

Jun draws an ellipse with a string and two pins at the foci. The long axis is 10 cm, and each pin is 4 cm from the center. What is the eccentricity e?
Kira draws an ellipse with a string and two tacks at the foci. The long axis is 26 cm, and each tack is 12 cm from the center. What is the eccentricity e?
Luz draws an ellipse with a hose and two stakes at the foci. The long axis is 20 ft, and each stake is 6 ft from the center. What is the eccentricity e?
Milo draws an ellipse with a rope and two posts at the foci. The long axis is 34 ft, and each post is 8 ft from the center. What is the eccentricity e?
5.
A comet's path past the Sun is modeled with eccentricity e = 1. Pia labels the path on a space poster. What kind of conic is the path?
- parabola
- hyperbola
- circle
6.
The object 'Oumuamua passed the Sun in 2017 on a path with eccentricity e = 1.2. Ren reads about it. What kind of conic is the path?
- parabola
- ellipse
- hyperbola
7.
Tala rides a Ferris wheel whose rim is a conic with eccentricity e = 0. What kind of conic is the rim?
- circle
- ellipse
- parabola
Zee sketches an oval rug as an ellipse with a = 5 and b = 4, half the long and short axes. How far is each focus from the center?
Jun sketches an oval kite as an ellipse with a = 13 and b = 5, half the long and short axes. How far is each focus from the center?
Kira sketches an oval table top as an ellipse with a = 10 and b = 8, half the long and short axes. How far is each focus from the center?

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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