Make equations for the circle. ### Understanding Coordinates and Circles on a Cartesian Plane#### IntroductionThis diagram illustrates two circles plotted on a Cartesian coordinate plane, which is a standard graphical representation of algebraic equations. The circles are labeled as $ C $ and $ D $.#### Diagram Description1. **Cartesian Coordinate Plane**: - The horizontal line represents the X-axis, labeled with tick marks extending from -4 to 4. - The vertical line represents the Y-axis, labeled similarly from -4 to 4. - The origin, the point where the X and Y axes intersect, is labeled as $ O $.2. **Circle $ D $**: - Circle $ D $ is centered at approximately $(0, 3)$. - The radius of circle $ D $ extends from $(0, 3)$ to about $(0, 7)$ or $(0, -1)$, indicating a radius of 4 units.3. **Circle $ C $**: - Circle $ C $ is centered at approximately $(2, -2)$. - The radius of circle $ C $ extends from $(2, -2)$ to about $(3, -2)$ or $(1, -2)$, indicating a radius of 1 unit.#### Analysis of the Diagram- The circles illustrate basic properties of shapes on a Cartesian plane, such as their radii and their centers’ coordinates.- Circle $ D $ is larger than circle $ C $ and is positioned primarily in the upper part of the graph.- Circle $ C $ is notably smaller and located in the lower-right quadrant of the graph.#### ConclusionUnderstanding this diagram is fundamental in learning how to plot points and shapes accurately on a coordinate plane, which is essential in algebra and geometry. The centers and radii of the circles are clear, emphasizing the importance of coordinates in defining geometrical shapes.---This educational representation aims to help students grasp the basics of plotting and analyzing circles on a Cartesian plane.

Answered: Image /qna-images/answer/e1aed466-3aab-4a7a-9b72-9e0cc40ee7fc.jpg

Answered: D 34 Oト

Math

Geometry

D 34 Oト

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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Question

Make equations for the circle.

### Understanding Coordinates and Circles on a Cartesian Plane

#### Introduction
This diagram illustrates two circles plotted on a Cartesian coordinate plane, which is a standard graphical representation of algebraic equations. The circles are labeled as $ C $ and $ D $.

#### Diagram Description

1. **Cartesian Coordinate Plane**:
- The horizontal line represents the X-axis, labeled with tick marks extending from -4 to 4.
- The vertical line represents the Y-axis, labeled similarly from -4 to 4.
- The origin, the point where the X and Y axes intersect, is labeled as $ O $.

2. **Circle $ D $**:
- Circle $ D $ is centered at approximately $(0, 3)$.
- The radius of circle $ D $ extends from $(0, 3)$ to about $(0, 7)$ or $(0, -1)$, indicating a radius of 4 units.

3. **Circle $ C $**:
- Circle $ C $ is centered at approximately $(2, -2)$.
- The radius of circle $ C $ extends from $(2, -2)$ to about $(3, -2)$ or $(1, -2)$, indicating a radius of 1 unit.

#### Analysis of the Diagram

- The circles illustrate basic properties of shapes on a Cartesian plane, such as their radii and their centers’ coordinates.
- Circle $ D $ is larger than circle $ C $ and is positioned primarily in the upper part of the graph.
- Circle $ C $ is notably smaller and located in the lower-right quadrant of the graph.

#### Conclusion
Understanding this diagram is fundamental in learning how to plot points and shapes accurately on a coordinate plane, which is essential in algebra and geometry. The centers and radii of the circles are clear, emphasizing the importance of coordinates in defining geometrical shapes.

---

This educational representation aims to help students grasp the basics of plotting and analyzing circles on a Cartesian plane.

Two-dimensional figure measured in terms of radius. It is formed by a set of points that are at a constant or fixed distance from a fixed point in the center of the plane. The parts of the circle are circumference, radius, diameter, chord, tangent, secant, arc of a circle, and segment in a circle.

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