Ellipses Worksheets
Read standard-form conic equations to identify centers, vertices, dimensions and curve types.
Before you begin
Factor polynomials, use exponent laws and solve equations with domain restrictions.
Worked example
For (x + 1)²/100 + (y - 3)²/36 = 1, find the center, major-axis direction and semi-axis lengths.
- The center is read from the shifted squares.
- The larger denominator lies under x, so the major axis is horizontal.
- Square-root the denominators to find semi-axis lengths.
Answer: Center (-1, 3); horizontal major axis; semimajor 10, semiminor 6.
Check your result using the method in the example before moving to the next question.
Choose your level
These sets use the same exercise types and number ranges across level labels. Choose a fresh set for additional practice.
- Easy: Start with the preview and follow the worked example.
- Medium: Practice the same exercise types with a fresh numbered set.
- Hard: Use another set to practice explaining and checking your answers.
Questions and answer calculations checked on 2026-09-17. How we check worksheets. Free for personal and classroom use.
Preview and print an easy set
Try six questions below, or choose a full set at your level.
1
For (x + 3)²/225 + (y + 1)²/81 = 1, find the center, major-axis direction and semi-axis lengths.
2
For (x - 2)²/100 + (y + 5)²/36 = 1, find the center, major-axis direction and semi-axis lengths.
3
For (x - 3)²/25 + (y - 1)²/9 = 1, find the center, major-axis direction and semi-axis lengths.
4
For (x - 2)²/225 + (y + 3)²/81 = 1, find the center, major-axis direction and semi-axis lengths.
5
For (x - 1)²/100 + (y - 4)²/36 = 1, find the center, major-axis direction and semi-axis lengths.
6
For (x - 5)²/100 + (y - 4)²/36 = 1, find the center, major-axis direction and semi-axis lengths.
Answer Key
1. Center (-3, -1); horizontal major axis; semimajor 15, semiminor 9.2. Center (2, -5); horizontal major axis; semimajor 10, semiminor 6.3. Center (3, 1); horizontal major axis; semimajor 5, semiminor 3.4. Center (2, -3); horizontal major axis; semimajor 15, semiminor 9.5. Center (1, 4); horizontal major axis; semimajor 10, semiminor 6.6. Center (5, 4); horizontal major axis; semimajor 10, semiminor 6.