Free Printable WorksheetMathGeometryMath CurriculumG-GPE.A.1

GEO.143 Interpret circles in standard and general form Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Geometry Math worksheet provides structured practice on GEO.143 Interpret circles in standard and general form. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

GEO.143 Interpret circles in standard and general form - Primary standard selected for prompt fields in this prompt cell: CCSS G-GPE.A.1. Skill statement in this prompt cell: Select the correctly rewritten circle equation in standard form and identify the circle's center and radius. Associated standards listed with this skill in the curriculum source: CCSS G-GPE.A.1; FL MA.912.GR.7.2-7.3; VA G.PC.4; TEKS §111.41(c). 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

Geometry

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 GEO.143 Interpret circles in standard and general form skill assessments:

Problem 1Difficulty: Mastery

The coordinate graph shows the circle represented by 2x² + 2y² + 16x + 40y + 24 = 24. Which option correctly matches the graphed circle's standard-form equation, center, and radius?

A(x + 4)² + (y - 10)² = 116; center (-4, 10); radius sqrt(116)

B(x + 4)² + (y + 10)² = 116; center (-4, -10); radius sqrt(116)

C(x + 4)² + (y + 10)² = 116; center (-4, -10); radius 116

D(x + 4)² + (y + 10)² = 232; center (-4, -10); radius sqrt(232)

Solution & Explanation:First divide or simplify the equation to x² + y² + 8x + 20y = 0. Move the constant term to the right, then complete the square by adding 16 to the x-part and 100 to the y-part. This gives (x + 4)² + (y + 10)² = 116. In standard form, the center is (-4, -10), and because r² = 116, the radius is sqrt(116).

Problem 2Difficulty: Mastery

A circular garden boundary on a coordinate map is modeled by x² + y² - 16x - 16y = 0. Which option gives the standard form, center, and radius?

A(x - 8)² + (y - 8)² = 128; center (8, 8); radius sqrt(128)

B(x + 8)² + (y - 8)² = 128; center (-8, 8); radius sqrt(128)

C(x - 8)² + (y + 8)² = 128; center (8, -8); radius sqrt(128)

D(x - 8)² + (y - 8)² = 128; center (8, 8); radius 128

Solution & Explanation:Move the constant term to the right, then complete the square by adding 64 to the x-part and 64 to the y-part. This gives (x - 8)² + (y - 8)² = 128. In standard form, the center is (8, 8), and because r² = 128, the radius is sqrt(128).

Problem 3Difficulty: Mastery

A class is analyzing the scaled circle equation 3x² + 66x + 3y² - 6y - 24 = 0. Which final standard form and circle information are correct?

A(x - 11)² + (y + 1)² = 130; center (11, -1); radius sqrt(130)

B(x - 11)² + (y - 1)² = 130; center (11, 1); radius sqrt(130)

C(x + 11)² + (y + 1)² = 130; center (-11, -1); radius sqrt(130)

D(x + 11)² + (y - 1)² = 130; center (-11, 1); radius sqrt(130)

Solution & Explanation:First divide or simplify the equation to x² + y² + 22x - 2y - 8 = 0. Move the constant term to the right, then complete the square by adding 121 to the x-part and 1 to the y-part. This gives (x + 11)² + (y - 1)² = 130. In standard form, the center is (-11, 1), and because r² = 130, the radius is sqrt(130).

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QWhat grade level and standards does this worksheet align with?

This worksheet is designed specifically for Geometry Math students. It aligns with educational standard G-GPE.A.1 (Primary standard selected for prompt fields in this prompt cell: CCSS G-GPE.A.1. Skill statement in this prompt cell: Select the correctly rewritten circle equation in standard form and identify the circle's center and radius. Associated standards listed with this skill in the curriculum source: CCSS G-GPE.A.1; FL MA.912.GR.7.2-7.3; VA G.PC.4; TEKS §111.41(c). Use this prompt-provided wording as the supporting standard description for this workflow.).