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Understanding Circle Equations: Center and Radius Identification**

This mini-lesson focuses on the fundamental concepts related to circles in coordinate geometry. Students will learn how to identify the center and radius of a circle from its standard equation. The lesson provides various examples, including circles defined by specific equations, enabling learners to practice finding centers and radii. Key equations are explored, along with multiple-choice questions to reinforce comprehension. This lesson is aligned with MA.912.G.6.6, ensuring students can confidently interpret and analyze circle equations in the coordinate plane.

terence-shirley
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Understanding Circle Equations: Center and Radius Identification**

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  1. Geometry Mini-Lesson Circle C is defined by the equation: (x + 4.2)2 + (y − 5.1)2 = 36Which of the following identifies the center C (h, k) and radius of circle C? • C (4.2, −5.1), radius of 36 units • C (−4.2, 5.1), radius of 36 units • C (−4.2, 5.1), radius of 6 units • C (4.2, −5.1), radius of 6 units MA.912.G.6.6: Given the center and the radius, find the equation of a circle in the coordinate plane or given the equation of a circle in center-radius form, state the center and the radius of the circle.

  2. Geometry Mini-Lesson Circle E has center E (1.6, −2.4) and a radius of 4 units.Which of the following equations defines circle E? • (x −1.6)2 + (y + 2.4)2 = 2 • (x − 1.6)2 + (y + 2.4)2 = 16 • (x − 1.6)2 + (y + 2.4)2 = 4 • (x + 1.6)2 + (y − 2.4)2 = 16 MA.912.G.6.6: Given the center and the radius, find the equation of a circle in the coordinate plane or given the equation of a circle in center-radius form, state the center and the radius of the circle.

  3. Geometry Mini-Lesson Circle A is shown in the graph below. Which of the following equations defines circle A? • (x − 9)2 + (y − 5)2 = 25 • (x + 9)2 + (y + 5)2 = 25 • (x − 9)2 + (y − 5)2 = 5 • (x + 9)2 + (y + 5)2 = 5 MA.912.G.6.6: Given the center and the radius, find the equation of a circle in the coordinate plane or given the equation of a circle in center-radius form, state the center and the radius of the circle.

  4. Geometry Mini-Lesson Circle C is shown in the graph below. Which of the following equations defines circle C? • (x − 2.5)2 + (y + 0.5)2 = 20.25 • (x − 2.5)2 + (y + 0.5)2 = 9 • (x + 2.5)2 + (y − 0.5)2 = 20.25 • (x + 2.5)2 + (y − 0.5)2 = 9 MA.912.G.6.6: Given the center and the radius, find the equation of a circle in the coordinate plane or given the equation of a circle in center-radius form, state the center and the radius of the circle.

  5. Geometry Mini-Lesson Circle D is defined by the equation (x + 3.6)2 + (y − 2.9)2 = 49Which of the following identifies the center D (h, k) and radius of circle D? • D (−3.6, 2.9), radius of 49 units • D (3.6, −2.9), radius of 7 units • D (3.6, −2.9), radius of 49 units • D (−3.6, 2.9), radius of 7 units MA.912.G.6.6: Given the center and the radius, find the equation of a circle in the coordinate plane or given the equation of a circle in center-radius form, state the center and the radius of the circle.

  6. Geometry Mini-Lesson Circle F has center F (5.4, −3.9) and a radius of 9 units. Which of the following equations defines circle F? • (x − 5.4)2 + (y + 3.9)2 = 81 • (x − 5.4)2 + (y + 3.9)2 = 3 • (x − 5.4)2 + (y + 3.9)2 = 9 • (x + 5.4)2 + (y − 3.9)2 = 81 MA.912.G.6.6: Given the center and the radius, find the equation of a circle in the coordinate plane or given the equation of a circle in center-radius form, state the center and the radius of the circle.

  7. Geometry Mini-Lesson Circle B is shown in the graph below. Which of the following equations defines circle B? • (x − 5)2 + (y − 8)2 = 4 • (x − 5)2 + (y − 8)2 = 16 • (x + 5)2 + (y + 8)2 = 16 • (x + 5)2 + (y − 8)2 = 4 MA.912.G.6.6: Given the center and the radius, find the equation of a circle in the coordinate plane or given the equation of a circle in center-radius form, state the center and the radius of the circle.

  8. Geometry Mini-Lesson Circle D is shown in the graph below. Which of the following equations defines circle D? • (x + 1.5)2 + (y − 0.5)2 = 7 • (x + 1.5)2 + (y − 0.5)2 = 12.25 • (x − 1.5)2 + (y + 0.5)2 = 7 • (x − 1.5)2 + (y + 0.5)2 = 12.25 MA.912.G.6.6: Given the center and the radius, find the equation of a circle in the coordinate plane or given the equation of a circle in center-radius form, state the center and the radius of the circle.

  9. Geometry Mini-Lesson MA.912.G.6.6: Given the center and the radius, find the equation of a circle in the coordinate plane or given the equation of a circle in center-radius form, state the center and the radius of the circle.

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