Ellipses Worksheet 1 | 11th Grade Easy

Read standard-form conic equations to identify centers, vertices, dimensions and curve types.

easy: Start with the preview and follow the worked example.

15 problems · 25-30 minutes · Skills: conic sections, ellipses, graphing

About This Worksheet

This easy-level worksheet contains 15 problems designed for 11th Grade students practicing ellipses. Easy worksheets use simpler numbers and straightforward problem types to build confidence and reinforce foundational skills.

Factor polynomials, use exponent laws and solve equations with domain restrictions.

Read standard-form conic equations to identify centers, vertices, dimensions and curve types.
Check your result using the method in the example before moving to the next question.

How to Solve: Worked Example

Example Problem: For (x + 1)²/100 + (y - 3)²/36 = 1, find the center, major-axis direction and semi-axis lengths.

Solution Steps:

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.

Tip: Check your result using the method in the example before moving to the next question.

Paper Include separate answer key in PDF

For (x + 3)²/225 + (y + 1)²/81 = 1, find the center, major-axis direction and semi-axis lengths.

For (x - 2)²/100 + (y + 5)²/36 = 1, find the center, major-axis direction and semi-axis lengths.

For (x - 3)²/25 + (y - 1)²/9 = 1, find the center, major-axis direction and semi-axis lengths.

For (x - 2)²/225 + (y + 3)²/81 = 1, find the center, major-axis direction and semi-axis lengths.

For (x - 1)²/100 + (y - 4)²/36 = 1, find the center, major-axis direction and semi-axis lengths.

For (x - 5)²/100 + (y - 4)²/36 = 1, find the center, major-axis direction and semi-axis lengths.

For (x - 2)²/100 + (y + 0)²/36 = 1, find the center, major-axis direction and semi-axis lengths.

For (x + 4)²/100 + (y + 5)²/36 = 1, find the center, major-axis direction and semi-axis lengths.

For (x + 4)²/225 + (y - 2)²/81 = 1, find the center, major-axis direction and semi-axis lengths.

For (x + 1)²/400 + (y + 3)²/144 = 1, find the center, major-axis direction and semi-axis lengths.

For (x - 5)²/100 + (y + 4)²/36 = 1, find the center, major-axis direction and semi-axis lengths.

For (x - 5)²/225 + (y + 1)²/81 = 1, find the center, major-axis direction and semi-axis lengths.

For (x + 0)²/625 + (y - 5)²/225 = 1, find the center, major-axis direction and semi-axis lengths.

For (x - 2)²/625 + (y - 5)²/225 = 1, find the center, major-axis direction and semi-axis lengths.

For (x + 4)²/400 + (y + 1)²/144 = 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 6.7. Center (2, 0); horizontal major axis; semimajor 10, semiminor 6.8. Center (-4, -5); horizontal major axis; semimajor 10, semiminor 6.9. Center (-4, 2); horizontal major axis; semimajor 15, semiminor 9.10. Center (-1, -3); horizontal major axis; semimajor 20, semiminor 12.11. Center (5, -4); horizontal major axis; semimajor 10, semiminor 6.12. Center (5, -1); horizontal major axis; semimajor 15, semiminor 9.13. Center (0, 5); horizontal major axis; semimajor 25, semiminor 15.14. Center (2, 5); horizontal major axis; semimajor 25, semiminor 15.15. Center (-4, -1); horizontal major axis; semimajor 20, semiminor 12.

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Frequently Asked Questions

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Each subtopic has 10 worksheets: Worksheets 1-3 are Easy, 4-7 are Medium, and 8-10 are Hard. Start with Easy worksheets to build confidence, then progress to harder ones.

What skills does this conic sections worksheet cover?

This worksheet focuses on conic sections, ellipses, graphing. It is designed for 11th Grade students and provides structured practice through varied problem types with a worked example to guide students before they begin.

Can I use this worksheet in my classroom?

Yes. All worksheets on K12Worksheets are free for classroom use. You can print copies for your entire class. With 10 worksheets per subtopic at three difficulty levels, you have plenty of options for differentiated instruction and individualized practice.

How many problems are on this worksheet?

This worksheet contains 15 problems. It typically takes 25-30 minutes to complete. An answer key with all solutions is included so parents and teachers can check work quickly.