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

Pre CAL.107 Derive and Interpret Ellipse Equations Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Pre-Calculus Math worksheet provides structured practice on Pre CAL.107 Derive and Interpret Ellipse Equations. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

Pre-CAL.107 Derive and Interpret Ellipse Equations - 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 or description, determine center, vertices, axis lengths, and foci and select the correct 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.107 Derive and Interpret Ellipse Equations skill assessments:

Problem 1Difficulty: Mastery
Which standard form is equivalent to 16x2 + 9y2 - 160x + 54y + 337 = 0?
A(x - 5)2/9 + (y + 3)2/16 = 1
B(x - 5)2/16 + (y + 3)2/9 = 1
C(x + 5)2/9 + (y - 3)2/16 = 1
D(x - 5)2/144 + (y + 3)2/144 = 1
Solution & Explanation:Completing the square gives 16(x - 5)2 + 9(y + 3)2 = 144. Dividing by 144 gives (x - 5)2/9 + (y + 3)2/16 = 1.
Problem 2Difficulty: Mastery
An ellipse has foci (0, -12) and (0, 12) and major axis length 26. What is b2?
Solution & Explanation:The foci give c = 12 and the major axis length gives a = 13. Thus b2 = a2 - c2 = 169 - 144 = 25.
Problem 3Difficulty: Mastery
An ellipse has center (-5, -2), vertex (-5, 10), and focus (-5, 4). Which equation represents it?
A(x + 5)2/108 + (y + 2)2/144 = 1
B(x + 5)2/144 + (y + 2)2/108 = 1
C(x - 5)2/108 + (y - 2)2/144 = 1
D(x + 5)2/36 + (y + 2)2/144 = 1
Solution & Explanation:The major axis is vertical. The vertex gives a = 12 and the focus gives c = 6, so b2 = a2 - c2 = 144 - 36 = 108.

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Frequently Asked Questions

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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 or description, determine center, vertices, axis lengths, and foci and select the correct 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.).

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