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

NameDate

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

Noah graphs the ellipse x²/36 + y²/100 = 1 on a graphing app. What is its eccentricity e?
Pia graphs the ellipse x²/169 + y²/144 = 1 on a graphing app. What is its eccentricity e?
Ren graphs the ellipse x²/64 + y²/289 = 1 on a graphing app. What is its eccentricity e?
Tala graphs the hyperbola x²/16 − y²/9 = 1 on a graphing app. What is its eccentricity e?
Zee graphs the hyperbola y²/9 − x²/16 = 1 on a graphing app. What is its eccentricity e?
Kira graphs the hyperbola y²/64 − x²/225 = 1 on a graphing app. What is its eccentricity e?
An elliptical running track is 100 m long and 60 m wide. Luz measures how stretched it is. What is its eccentricity e?
A whispering gallery, an elliptical room, is 26 m long and 10 m wide. Milo measures how stretched it is. What is its eccentricity e?
An elliptical garden bed is 34 ft long and 16 ft wide. Noah measures how stretched it is. What is its eccentricity e?
An elliptical pond is 50 ft long and 14 ft wide. Pia measures how stretched it is. What is its eccentricity e?

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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