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

See similar textbooks

Related questions

Q: Determine the equation of the circle with radius 33 and center (−1,0).

A: circle with radius 33 and center (−1,0).

Q: Find the equation of the circle that passes through the points (2,13), (-14,-3) and (2,-19). Show…

Q: Write the standard form of the equation for the circle with center (-2,5) and radius √11. Graph…

Q: A circle has a diameter with endpoints (-2,1) and (22, 21). Find the coordinates of the center

A: Given endpoints of diameter of circle are (-2, 1) and (22, 21)

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.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Equations$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, geometry and related others by exploring similar questions and additional content below.

Similar questions

Write an equation of the circle with center (4, –3) and radius 8.
Does this equation represent a circle?
How would I draw the circles to these points?
Explain how to transform the equation of the circle from one form to another. Give an example.
Write the equation of the circle centered at (- 5, 8) with diameter 14.
Draw how far will a point travel if it goes (a) 1/4, (b) 1/12, (c) 3/8, and (d)5/6 of the way around theunit circle.
• Calculate = 3 +5 2-3 on the circle |z|