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: How would you recognize a nonstandard equation as a circle?

A: Equation of a circle will contain the terms x2 & y2 with same coefficients.

Q: Find the equation of the circle in the figure. Center

Q: how is the equation for a circle written?

A: Let us take center of the circle as (h,k) and radius = r.

Q: Find an equation of the circle whose diameter has endpoints (-4, 3) and (6, – 1). O=0

A: Recall: Equation of the circle : x-h2 +y-k2=r2 ; (h,k) is the center and 'r' is the radius.

Q: Write an equation of the circle with center (9, -3) and radius 5. D=0

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

Q: 20. (8. 7) and (-10, -13)

Q: Write the equation of circle with the following characteristics: Center at (1,7) and the circle has…

A: Given:- center (1,7) and area lf circle is 25π To find:- Equation of circle with given conditions

Q: ++ 2. 4. -2

Q: What are the two forms of the equation of a circle? Briey describe in words how you would go from…

A: Definition of a Circle A circle is the set of all points in a plane equidistant from a fixed point…

Q: Write the equation in standard form for the circle that has and (0, -3). diameter with endpoints (C

Q: graph the circle using its end points (-2, -8) & (0,0)

A: Solving the problem by finding the graph of the equation.

Q: What is the center of the circle represented by the equation?

A: Given data: The given expression is 3x2+12x+3y2-6y-33=0. The given expression can be written as,…

Q: Given a circle with center at (-2, 5) and diameter of 16, write an equation to represent this…

A: The equation of a circle is (x-a)2 + (y-b)2 = r2, where (a,b) is the centre of the circle, and r is…

Q: Does this equation represent a circle

Q: How would I draw the circles to these points?

A: (1) It is known that, the standard form of the equation of a circle with the center at (0,0) is,x2 +…

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.