Conic sections
Properties of ellipses worksheets
Find exact centers, vertices, co-vertices, foci, axis lengths and eccentricity from standard-form ellipse equations.
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Writing equations of ellipses worksheets
Construct exact standard-form ellipse equations from vertices, co-vertices, foci, centers and horizontal widths.
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Use the given information to write each ellipse in standard form.
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Build an ellipse from exact geometric data
Each worksheet contains ten constructions selected from nine source-backed given forms.
Find the common center and axial squared distances, then place the horizontal and vertical semiaxis squares under the matching terms. Horizontal width always means twice the horizontal semiaxis.
The separate key gives the exact standard equation for every construction.
Learning objective
What this activity builds
Use exact geometric data to determine an axis-aligned ellipse in standard form.
Worked example
Write the ellipse centered at (0, 0) with vertex (5, 0) and co-vertex (0, 3).
x²/25 + y²/9 = 1.
The horizontal and vertical semiaxes are 5 and 3, so their squared denominators are 25 and 9.
Teaching notes
Make the practice count
- Find the common center before measuring axial distances.
- Use a² = b² + c² when foci and minor endpoints are given.
- Horizontal width always determines twice the horizontal radius.
- Check that major and minor data are perpendicular.
Make it yours
Customize the practice
Choose your options, update the preview, then download the exact same pages.
Choose one or more construction forms, then change the seed for ten reproducible ellipse equations.
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