Free Printable WorksheetMathPre-CalculusMath CurriculumHSG-GPE.A.1-3(+)

Pre CAL.117 Determine Foci, Vertices, and Axes for Ellipses Worksheet

Download our free printable Pre-Calculus Math worksheet on Pre CAL.117 Determine Foci, Vertices, and Axes for Ellipses. Ideal for classroom practice, homeschool learning, independent homework, and standardized test preparation. Available in both print-ready PDF and editable DOCX formats.

Choose your preferred download format:

100% Free • No registration or login required • Instant file access

Download PDF Download DOCX

Prefer interactive practice with instant grading and explanations?Practice Determine Foci, Vertices, and Axes for Ellipses Online

Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Pre-Calculus Math worksheet provides structured practice on Pre CAL.117 Determine Foci, Vertices, and Axes for Ellipses. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

Pre-CAL.117 Determine Foci, Vertices, and Axes for Ellipses - Primary standard selected for prompt fields in this prompt cell: CCSS HSG-GPE.A.1-3(+). Skill statement in this prompt cell: Given an ellipse equation, identify vertices, foci, and axis lengths and select the correct labeled graph. Associated standards listed with this skill in this prompt cell: CCSS HSG-GPE.A.1-3(+); CCSS HS-Modeling; SMP 1,2,4,5,7,8; AP Precalculus CED Units 3-4; TX §111.42(c)(3)(D-H); FL MA.912.GR.7.1-7.9, MA.912.T.4.5-4.7; VA MA.AG.1-2. Use this prompt-provided wording as the supporting standard description for this workflow.

Whether you are an educator preparing classroom handouts, a tutor reinforcing weekly topics, or a parent supporting homeschool learning, this printable resource gives students the deliberate practice required to achieve subject fluency and master state standards.

Grade

Pre-Calculus

Subject

Math

Domain

Math Curriculum

Formats

PDF & DOCX

Sample Practice Problems

Preview the types of problems and questions covered in this worksheet

Below are sample questions representative of the exercises included on this worksheet and related Pre CAL.117 Determine Foci, Vertices, and Axes for Ellipses skill assessments:

Problem 1Difficulty: Mastery

For the ellipse 225x² + 64y² + 5850x - 896y + 26761 = 0, which statement gives the center and direction of the major axis?

Acenter (13, -7); major axis is vertical

Bcenter (-13, 7); major axis is vertical

Ccenter (-13, 7); major axis is horizontal

Dcenter (13, -7); major axis is horizontal

Solution & Explanation:Complete the square to rewrite the equation as (x + 13)²/64 + (y - 7)²/225 = 1. The squared terms show the center (-13, 7). The largest denominator, 225, is under the y-term, so the major axis is vertical.

Problem 2Difficulty: Mastery

For the ellipse 49x² + 144y² - 490x - 3456y + 14905 = 0, which points are the foci?

A(-7, 12) and (17, 12)

B(5, 12 - sqrt(95)) and (5, 12 + sqrt(95))

C(5 - sqrt(193), 12) and (5 + sqrt(193), 12)

D(5 - sqrt(95), 12) and (5 + sqrt(95), 12)

Solution & Explanation:Complete the square to rewrite the equation as (x - 5)²/144 + (y - 12)²/49 = 1. The center is (5, 12). The larger denominator is 144, so the major axis is horizontal. Use c² = a² - b² = 144 - 49 = 95. Since the foci lie on the major axis, the foci are (5 - sqrt(95), 12) and (5 + sqrt(95), 12).

Problem 3Difficulty: Mastery

For the ellipse 121x² + 36y² + 2420x + 576y + 10048 = 0, which option correctly gives the vertices, foci, and axis lengths?

Avertices (-16, -8) and (-4, -8); foci (-10 - sqrt(85), -8) and (-10 + sqrt(85), -8); major axis length 22; minor axis length 12

Bvertices (-10, -19) and (-10, 3); foci (-10, -8 - sqrt(157)) and (-10, -8 + sqrt(157)); major axis length 22; minor axis length 12

Cvertices (-10, -19) and (-10, 3); foci (-10, -8 - sqrt(85)) and (-10, -8 + sqrt(85)); major axis length 22; minor axis length 12

Dvertices (10, -3) and (10, 19); foci (10, 8 - sqrt(85)) and (10, 8 + sqrt(85)); major axis length 22; minor axis length 12

Solution & Explanation:Complete the square to rewrite the equation as (x + 10)²/36 + (y + 8)²/121 = 1. The center is (-10, -8). The larger denominator is 121, so the major axis is vertical. Use c² = a² - b² = 121 - 36 = 85. Therefore the vertices are (-10, -19) and (-10, 3), the foci are (-10, -8 - sqrt(85)) and (-10, -8 + sqrt(85)), and the axis lengths are 22 and 12.

Want more practice questions with step-by-step guidance?

Practice All Questions Online

Frequently Asked Questions

Common questions about printing, using, and solving this worksheet

QHow do I download and print this Pre CAL.117 Determine Foci, Vertices, and Axes for Ellipses worksheet?

Click either the "Download PDF" or "Download DOCX" button at the top of the page. You can print the PDF directly from your browser or edit the DOCX file in Microsoft Word or Google Docs to tailor the questions to your students.

QIs this Pre CAL.117 Determine Foci, Vertices, and Axes for Ellipses worksheet free for teachers and homeschoolers?

Yes! All learning materials, worksheets, and practice resources on Free K12 Practice are 100% free for teachers, students, parents, tutors, and homeschooling families for non-commercial educational use. No account or subscription is required.

QCan students practice Pre CAL.117 Determine Foci, Vertices, and Axes for Ellipses online with instant feedback?

Yes! In addition to this printable worksheet, students can practice Pre CAL.117 Determine Foci, Vertices, and Axes for Ellipses interactively on our platform with automated grading, instant score tracking, and detailed step-by-step solutions.

QWhat grade level and standards does this worksheet align with?

This worksheet is designed specifically for Pre-Calculus Math students. It aligns with educational standard HSG-GPE.A.1-3(+) (Primary standard selected for prompt fields in this prompt cell: CCSS HSG-GPE.A.1-3(+). Skill statement in this prompt cell: Given an ellipse equation, identify vertices, foci, and axis lengths and select the correct labeled graph. Associated standards listed with this skill in this prompt cell: CCSS HSG-GPE.A.1-3(+); CCSS HS-Modeling; SMP 1,2,4,5,7,8; AP Precalculus CED Units 3-4; TX §111.42(c)(3)(D-H); FL MA.912.GR.7.1-7.9, MA.912.T.4.5-4.7; VA MA.AG.1-2. Use this prompt-provided wording as the supporting standard description for this workflow.).