### Equation of a Semi-Circle **Task:** Find the equation of the semi-circle pictured. **Graph Description:** The graph displays a semi-circle centered at the point \((-3, 3)\) on a coordinate plane. The semi-circle extends from \((-5, 3)\) to \((-1, 3)\) on the x-axis, with its arc reaching up to \(y = 1\). This semi-circle is oriented such that it opens downwards. **Steps to Find the Equation:** 1. **Identify the Center:** The center of the semi-circle is at \((-3, 3)\). 2. **Determine the Radius:** The distance from the center to the edge along the x-axis is 2 units, indicating that the radius is 2. 3. **Equation of a Semi-Circle:** For a semicircle opening downwards with the center at \((h, k)\) and radius \(r\), the standard form of the equation is: \[ (x - h)^2 + (y - k)^2 = r^2 \] Given: - \(h = -3\) - \(k = 3\) - \(r = 2\) 4. **Plug in the Values:** \[ (x + 3)^2 + (y - 3)^2 = 2^2 \] 5. **Simplified Equation:** \[ (x + 3)^2 + (y - 3)^2 = 4 \] **Note:** This represents the full circle. To express the equation for only the upper half (semi-circle), solve for \(y\) in terms of \(x\) for the top half: \[ y = 3 - \sqrt{4 - (x + 3)^2} \] **Input Box:** An input box is provided to enter the equation. After inputting the equation, you can click the "Submit Question" button. **URL Source (not clickable):** `https://www.myopenmath.com/assess2/#/skip/9`
### Equation of a Semi-Circle **Task:** Find the equation of the semi-circle pictured. **Graph Description:** The graph displays a semi-circle centered at the point \((-3, 3)\) on a coordinate plane. The semi-circle extends from \((-5, 3)\) to \((-1, 3)\) on the x-axis, with its arc reaching up to \(y = 1\). This semi-circle is oriented such that it opens downwards. **Steps to Find the Equation:** 1. **Identify the Center:** The center of the semi-circle is at \((-3, 3)\). 2. **Determine the Radius:** The distance from the center to the edge along the x-axis is 2 units, indicating that the radius is 2. 3. **Equation of a Semi-Circle:** For a semicircle opening downwards with the center at \((h, k)\) and radius \(r\), the standard form of the equation is: \[ (x - h)^2 + (y - k)^2 = r^2 \] Given: - \(h = -3\) - \(k = 3\) - \(r = 2\) 4. **Plug in the Values:** \[ (x + 3)^2 + (y - 3)^2 = 2^2 \] 5. **Simplified Equation:** \[ (x + 3)^2 + (y - 3)^2 = 4 \] **Note:** This represents the full circle. To express the equation for only the upper half (semi-circle), solve for \(y\) in terms of \(x\) for the top half: \[ y = 3 - \sqrt{4 - (x + 3)^2} \] **Input Box:** An input box is provided to enter the equation. After inputting the equation, you can click the "Submit Question" button. **URL Source (not clickable):** `https://www.myopenmath.com/assess2/#/skip/9`
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
Related questions
Question
![### Equation of a Semi-Circle
**Task:**
Find the equation of the semi-circle pictured.
**Graph Description:**
The graph displays a semi-circle centered at the point \((-3, 3)\) on a coordinate plane. The semi-circle extends from \((-5, 3)\) to \((-1, 3)\) on the x-axis, with its arc reaching up to \(y = 1\). This semi-circle is oriented such that it opens downwards.
**Steps to Find the Equation:**
1. **Identify the Center:**
The center of the semi-circle is at \((-3, 3)\).
2. **Determine the Radius:**
The distance from the center to the edge along the x-axis is 2 units, indicating that the radius is 2.
3. **Equation of a Semi-Circle:**
For a semicircle opening downwards with the center at \((h, k)\) and radius \(r\), the standard form of the equation is:
\[
(x - h)^2 + (y - k)^2 = r^2
\]
Given:
- \(h = -3\)
- \(k = 3\)
- \(r = 2\)
4. **Plug in the Values:**
\[
(x + 3)^2 + (y - 3)^2 = 2^2
\]
5. **Simplified Equation:**
\[
(x + 3)^2 + (y - 3)^2 = 4
\]
**Note:**
This represents the full circle. To express the equation for only the upper half (semi-circle), solve for \(y\) in terms of \(x\) for the top half:
\[
y = 3 - \sqrt{4 - (x + 3)^2}
\]
**Input Box:**
An input box is provided to enter the equation. After inputting the equation, you can click the "Submit Question" button.
**URL Source (not clickable):**
`https://www.myopenmath.com/assess2/#/skip/9`](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff07f1948-7bc7-44b0-b956-514fa1b4223b%2F42e4de68-dbdb-4f38-8fa2-c5fd31619ab0%2Fi26c69k.jpeg&w=3840&q=75)
Transcribed Image Text:### Equation of a Semi-Circle
**Task:**
Find the equation of the semi-circle pictured.
**Graph Description:**
The graph displays a semi-circle centered at the point \((-3, 3)\) on a coordinate plane. The semi-circle extends from \((-5, 3)\) to \((-1, 3)\) on the x-axis, with its arc reaching up to \(y = 1\). This semi-circle is oriented such that it opens downwards.
**Steps to Find the Equation:**
1. **Identify the Center:**
The center of the semi-circle is at \((-3, 3)\).
2. **Determine the Radius:**
The distance from the center to the edge along the x-axis is 2 units, indicating that the radius is 2.
3. **Equation of a Semi-Circle:**
For a semicircle opening downwards with the center at \((h, k)\) and radius \(r\), the standard form of the equation is:
\[
(x - h)^2 + (y - k)^2 = r^2
\]
Given:
- \(h = -3\)
- \(k = 3\)
- \(r = 2\)
4. **Plug in the Values:**
\[
(x + 3)^2 + (y - 3)^2 = 2^2
\]
5. **Simplified Equation:**
\[
(x + 3)^2 + (y - 3)^2 = 4
\]
**Note:**
This represents the full circle. To express the equation for only the upper half (semi-circle), solve for \(y\) in terms of \(x\) for the top half:
\[
y = 3 - \sqrt{4 - (x + 3)^2}
\]
**Input Box:**
An input box is provided to enter the equation. After inputting the equation, you can click the "Submit Question" button.
**URL Source (not clickable):**
`https://www.myopenmath.com/assess2/#/skip/9`
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