## Finding the Center and Radius of a Circle and Graphing the CircleThe equation of a circle is $(x - 2)^2 + (y - 4)^2 = 4$. Find the center and the radius of the circle. Then graph the circle.1. The given equation of the circle is $(x - 2)^2 + (y - 4)^2 = 4$. - **Center:** $(2, 4)$ - **Radius:** The radius is the square root of the right-hand side of the equation. Since $4 = 2^2$, the radius $r = 2$.2. Graphing the circles: - **First Graph:** - **Center:** $(2, 4)$ - **Radius:** $4$ - **Explanation:** The graph shows a circle centered at point $(2, 4)$ with a radius of 4 units. The circle is drawn on a coordinate plane with the x-axis and y-axis ranging from $-10$ to $10$. - **Second Graph:** - **Center:** $(4, 2)$ - **Radius:** $4$ - **Explanation:** The graph displays a circle centered at $(4, 2)$ with a radius of 4 units. This circle is similarly drawn with the coordinates laid out on a plane extending from $-10$ to $10$. - **Third Graph:** - **Center:** $(-2, -4)$ - **Radius:** $2$ - **Explanation:** The final graph shows a circle centered at $(-2, -4)$ with a radius of 2 units. This graph also follows the same coordinate layout ranging from $-10$ to $10$.The diagrams illustrate how to plot the circles with their respective centers and radii on a coordinate plane. Each graph clearly indicates the position and size of the circles.**Visual Aids:**- **Graph 1:** A circle centered at (2,4) with a radius of 4.- **Graph 2:** A circle centered at (4,2) with a radius of 4.- **Graph 3:** A circle centered at (-2,-4) with a radius of 2.Understanding how to

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The equation of a circle is X-2) +-4) =4 Find the center and the radius of the circle. Then graph the circle. = 4 center: ( 4), radius: 4 10 1D center: (4, 4), radius: 4 10-

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

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## Finding the Center and Radius of a Circle and Graphing the Circle

The equation of a circle is $(x - 2)^2 + (y - 4)^2 = 4$. Find the center and the radius of the circle. Then graph the circle.

1. The given equation of the circle is $(x - 2)^2 + (y - 4)^2 = 4$.

- **Center:** $(2, 4)$
- **Radius:** The radius is the square root of the right-hand side of the equation. Since $4 = 2^2$, the radius $r = 2$.

2. Graphing the circles:

- **First Graph:**
- **Center:** $(2, 4)$
- **Radius:** $4$
- **Explanation:** The graph shows a circle centered at point $(2, 4)$ with a radius of 4 units. The circle is drawn on a coordinate plane with the x-axis and y-axis ranging from $-10$ to $10$.

- **Second Graph:**
- **Center:** $(4, 2)$
- **Radius:** $4$
- **Explanation:** The graph displays a circle centered at $(4, 2)$ with a radius of 4 units. This circle is similarly drawn with the coordinates laid out on a plane extending from $-10$ to $10$.

- **Third Graph:**
- **Center:** $(-2, -4)$
- **Radius:** $2$
- **Explanation:** The final graph shows a circle centered at $(-2, -4)$ with a radius of 2 units. This graph also follows the same coordinate layout ranging from $-10$ to $10$.

The diagrams illustrate how to plot the circles with their respective centers and radii on a coordinate plane. Each graph clearly indicates the position and size of the circles.

**Visual Aids:**
- **Graph 1:** A circle centered at (2,4) with a radius of 4.
- **Graph 2:** A circle centered at (4,2) with a radius of 4.
- **Graph 3:** A circle centered at (-2,-4) with a radius of 2.

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