a.) What kind of line intersects the larger circle a secant or tangent ? b.) if tangent name the point of tangency c.) name the line using two letters d.) write the equation of this line

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
icon
Related questions
icon
Concept explainers
Question
a.) What kind of line intersects the larger circle a secant or tangent ? b.) if tangent name the point of tangency c.) name the line using two letters d.) write the equation of this line
### Coordinate Geometry - Understanding the Graph 

In the attached graph, we have a coordinate plane with two circles displayed on a grid.

#### Elements of the Graph:
1. **Axes**: 
   - The horizontal axis is the **x-axis**.
   - The vertical axis is the **y-axis**.
   - Both axes intersect at (0,0), which is the origin of the coordinate system.

2. **Grid**: 
   - The entire graph is overlaid with a grid that helps in identifying the coordinates of points.
   - Each square in the grid represents a unit distance on the x and y axes.

3. **Circles**:
    - **Larger Circle**:
      - This circle is centered at point **P**, located at (-2, 1).
      - The radius of this circle appears to be 4 units as it extends from the center to approximately (2, 1) and (-6, 1).
      
    - **Smaller Circle**:
      - This circle is centered at point **Z**, situated at (3, -3).
      - The radius of this circle is 2 units as it extends from the center to roughly (5, -3) and (1, -3).

4. **Highlighted Points**:
   - **P**: Center of the larger circle at coordinates (-2, 1).
   - **Z**: Center of the smaller circle at coordinates (3, -3).
   - **A, B, C**: These points are marked on the axes:
      - **A**: Positioned on the x-axis at (-5, 0).
      - **B**: Positioned on the x-axis at (5, 0).
      - **C**: Positioned on the y-axis at (0, 5).

5. **Arrows**:
   - The ends of the x and y axes have arrows indicating the positive directions.
   - Points A, B, and C have arrows suggesting additional boundaries or highlighted regions on the axes.

The graph serves as a typical example used in coordinate geometry to help students understand how to plot points, analyze circles, and interpret the position of points relative to each other on a coordinate plane. Understanding these fundamental concepts is essential for learning more advanced topics in mathematics.
Transcribed Image Text:### Coordinate Geometry - Understanding the Graph In the attached graph, we have a coordinate plane with two circles displayed on a grid. #### Elements of the Graph: 1. **Axes**: - The horizontal axis is the **x-axis**. - The vertical axis is the **y-axis**. - Both axes intersect at (0,0), which is the origin of the coordinate system. 2. **Grid**: - The entire graph is overlaid with a grid that helps in identifying the coordinates of points. - Each square in the grid represents a unit distance on the x and y axes. 3. **Circles**: - **Larger Circle**: - This circle is centered at point **P**, located at (-2, 1). - The radius of this circle appears to be 4 units as it extends from the center to approximately (2, 1) and (-6, 1). - **Smaller Circle**: - This circle is centered at point **Z**, situated at (3, -3). - The radius of this circle is 2 units as it extends from the center to roughly (5, -3) and (1, -3). 4. **Highlighted Points**: - **P**: Center of the larger circle at coordinates (-2, 1). - **Z**: Center of the smaller circle at coordinates (3, -3). - **A, B, C**: These points are marked on the axes: - **A**: Positioned on the x-axis at (-5, 0). - **B**: Positioned on the x-axis at (5, 0). - **C**: Positioned on the y-axis at (0, 5). 5. **Arrows**: - The ends of the x and y axes have arrows indicating the positive directions. - Points A, B, and C have arrows suggesting additional boundaries or highlighted regions on the axes. The graph serves as a typical example used in coordinate geometry to help students understand how to plot points, analyze circles, and interpret the position of points relative to each other on a coordinate plane. Understanding these fundamental concepts is essential for learning more advanced topics in mathematics.
Expert Solution
steps

Step by step

Solved in 2 steps

Blurred answer
Knowledge Booster
Points, Lines and Planes
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.
Recommended textbooks for you
Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Elementary Geometry for College Students
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning