Transcribed Image Text:**Title: Writing Equations of Circles**
In this exercise, we will learn how to write the equations that represent two given circles on a coordinate plane.
**Problem 1:**
Observe the first circle graph:
1. **Description:**
- The center of the circle is located at (-2, 4).
- The circle passes through several points, but notably through the number 6 on the y-axis and -2 on the x-axis, showing that the radius extends from -2 to 4, up to -2 to 8.
- Radius: The radius can be identified as the distance from the center to the perimeter of the circle. Here, it has a length of 4 units.
**Graph Details:**
- The x-axis ranges from -7 to 2.
- The y-axis ranges from 0 to 8.
- The circle is centered at (-2, 4) and has a radius of 4.
**Equation:**
Using the standard equation for a circle \((x - h)^2 + (y - k)^2 = r^2\), where \((h, k)\) is the center and \(r\) is the radius, we substitute the values:
- Center \((h, k) = (-2, 4)\)
- Radius \(r = 4\)
So, the equation for the first circle is:
\[
(x + 2)^2 + (y - 4)^2 = 16
\]
**Problem 2:**
Observe the second circle graph:
2. **Description:**
- The center of the circle is located at (0, 0), which is the origin.
- The circle passes through several points, extending 8 units in every direction from the center, confirming that the radius is 8 units.
**Graph Details:**
- The x-axis ranges from -8 to 8.
- The y-axis ranges from -8 to 8.
- The circle is centered at the origin (0, 0) and has a radius of 8.
**Equation:**
Using the standard equation for a circle \((x - h)^2 + (y - k)^2 = r^2\), where \((h, k)\) is the center and \(r\) is the radius, we substitute the values:
- Center \((h,
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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![**Title: Writing Equations of Circles**
In this exercise, we will learn how to write the equations that represent two given circles on a coordinate plane.
**Problem 1:**
Observe the first circle graph:
1. **Description:**
- The center of the circle is located at (-2, 4).
- The circle passes through several points, but notably through the number 6 on the y-axis and -2 on the x-axis, showing that the radius extends from -2 to 4, up to -2 to 8.
- Radius: The radius can be identified as the distance from the center to the perimeter of the circle. Here, it has a length of 4 units.
**Graph Details:**
- The x-axis ranges from -7 to 2.
- The y-axis ranges from 0 to 8.
- The circle is centered at (-2, 4) and has a radius of 4.
**Equation:**
Using the standard equation for a circle \((x - h)^2 + (y - k)^2 = r^2\), where \((h, k)\) is the center and \(r\) is the radius, we substitute the values:
- Center \((h, k) = (-2, 4)\)
- Radius \(r = 4\)
So, the equation for the first circle is:
\[
(x + 2)^2 + (y - 4)^2 = 16
\]
**Problem 2:**
Observe the second circle graph:
2. **Description:**
- The center of the circle is located at (0, 0), which is the origin.
- The circle passes through several points, extending 8 units in every direction from the center, confirming that the radius is 8 units.
**Graph Details:**
- The x-axis ranges from -8 to 8.
- The y-axis ranges from -8 to 8.
- The circle is centered at the origin (0, 0) and has a radius of 8.
**Equation:**
Using the standard equation for a circle \((x - h)^2 + (y - k)^2 = r^2\), where \((h, k)\) is the center and \(r\) is the radius, we substitute the values:
- Center \((h,](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1b489826-5180-4405-9e86-63fd9ca11119%2Fbd94c458-1ee4-4336-aab7-b4f8909410ca%2Fd7hgjgj_processed.png&w=3840&q=75)
