Write the standard form of the equation of the circle with the graph shown to the right. What is the standard form of the equation of the circle to the right?
Write the standard form of the equation of the circle with the graph shown to the right. What is the standard form of the equation of the circle to the right?
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter1: Equations And Graphs
Section1.CR: Chapter Review
Problem 5CC: a How do you test whether the graph of an equation is symmetric with respect to the i x-axis, ii...
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![**Geometry Lesson 12.5.17: Finding the Standard Form of a Circle's Equation**
**Objective:**
Write the standard form of the equation of the circle using the given graph.
**Problem Statement:**
"Write the standard form of the equation of the circle with the graph shown to the right. What is the standard form of the equation of the circle to the right?"
**Graph Analysis:**
The graph provided displays a circle plotted on a coordinate plane. The circle’s center appears to be at the coordinate point \((3, -5)\) and its radius seems to be 2 units, based on the grid.
**Solution:**
The standard form of a circle’s equation is:
\[ (x - h)^2 + (y - k)^2 = r^2 \]
where \((h, k)\) is the center of the circle and \(r\) is the radius.
From the graph:
- Center \((h, k) = (3, -5)\)
- Radius \(r = 2\)
Plugging these values into the standard form equation:
\[ (x - 3)^2 + (y + 5)^2 = 2^2 \]
\[ (x - 3)^2 + (y + 5)^2 = 4 \]
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Transcribed Image Text:**Geometry Lesson 12.5.17: Finding the Standard Form of a Circle's Equation**
**Objective:**
Write the standard form of the equation of the circle using the given graph.
**Problem Statement:**
"Write the standard form of the equation of the circle with the graph shown to the right. What is the standard form of the equation of the circle to the right?"
**Graph Analysis:**
The graph provided displays a circle plotted on a coordinate plane. The circle’s center appears to be at the coordinate point \((3, -5)\) and its radius seems to be 2 units, based on the grid.
**Solution:**
The standard form of a circle’s equation is:
\[ (x - h)^2 + (y - k)^2 = r^2 \]
where \((h, k)\) is the center of the circle and \(r\) is the radius.
From the graph:
- Center \((h, k) = (3, -5)\)
- Radius \(r = 2\)
Plugging these values into the standard form equation:
\[ (x - 3)^2 + (y + 5)^2 = 2^2 \]
\[ (x - 3)^2 + (y + 5)^2 = 4 \]
**Interactive Component:**
*Enter your answer in the box below and click "Check Answer."*
[Input Box]
[Check Answer Button]
**Note:**
All parts showing.
[Clear All Button]
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