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Conic sections practice

Eccentricity of conic sections worksheets

Find exact eccentricities for circles, ellipses, parabolas and hyperbolas from standard or general equations.

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Find the exact eccentricity of each conic section.

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Compare conics through eccentricity

Each worksheet contains twelve circles, ellipses, parabolas or hyperbolas in standard, general or mixed form.

Exact eccentricity is 0 for circles, 1 for parabolas, between 0 and 1 for ellipses and greater than 1 for hyperbolas.

The key keeps rational and radical values exact and identifies each conic type.

Learning objective

What this activity builds

Connect each conic equation with its exact focal-distance ratio.

Worked example

Find the eccentricity of x²/25 + y²/9 = 1.

e = 4/5.

For the ellipse, c² = 25 − 9 = 16 and e = c/a = 4/5.

Teaching notes

Make the practice count

  • A circle has eccentricity 0.
  • A parabola has eccentricity 1.
  • Ellipse eccentricity lies between 0 and 1.
  • Hyperbola eccentricity is greater than 1.

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Choose conic types and standard, general or mixed equations for twelve reproducible exact eccentricities.

Worksheet settings

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Math SheetNameScore/ 12TeacherDateEccentricity of Conic SectionsFind the exact eccentricity of each conic section.1.x+529-1·y-221=1e = ____________________2.x=y2-5e = ____________________3.x-429+y-3216=1e = ____________________4.x-32+y+42=36e = ____________________5.x+2236-1·y-5216=1e = ____________________6.x=2·y2-5e = ____________________math-sheet.comPage 1 / 2
Math SheetNameScore/ 12TeacherDateEccentricity of Conic SectionsFind the exact eccentricity of each conic section.7.x-524+y-129=1e = ____________________8.x+32+y+52=1e = ____________________9.x-229-1·y-4236=1e = ____________________10.x=-5·y-52+1e = ____________________11.x+4216+y+4225=1e = ____________________12.x-32+y+32=9e = ____________________math-sheet.comPage 2 / 2

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