Identify The Center Of The Circle { (x+1)^2 + (y-3)^2 = 16$}$.A. { (1, 3)$}$B. { (-1, -3)$}$C. { (-1, 3)$}$D. { (1, -3)$}$

Introduction

In mathematics, a circle is a set of points that are all equidistant from a central point known as the center. The equation of a circle in standard form is given by ${(x-h)^2 + (y-k)^2 = r^2}$, where ${(h, k)}$ represents the coordinates of the center of the circle, and ${r}$ is the radius. In this article, we will focus on identifying the center of a circle given its equation.

Understanding the Equation of a Circle

The equation of a circle in standard form is ${(x-h)^2 + (y-k)^2 = r^2}$. To identify the center of the circle, we need to look at the values of ${h}$ and ${k}$ in the equation. The values of ${h}$ and ${k}$ represent the x-coordinate and y-coordinate of the center of the circle, respectively.

Identifying the Center of the Given Circle

The given equation of the circle is ${(x+1)^2 + (y-3)^2 = 16}$. To identify the center of the circle, we need to look at the values of ${h}$ and ${k}$ in the equation. In this case, ${h = -1}$ and ${k = 3}$. Therefore, the center of the circle is ${(-1, 3)}$.

Conclusion

In conclusion, identifying the center of a circle is a straightforward process that involves looking at the values of ${h}$ and ${k}$ in the equation of the circle. By following the steps outlined in this article, you can easily identify the center of a circle given its equation.

Answer

The correct answer is ${(-1, 3)}$.

Discussion

• What is the equation of a circle in standard form?
• How do you identify the center of a circle given its equation?
• What are the values of ${h}$ and ${k}$ in the equation of a circle?

Related Topics

• Equation of a circle
• Center of a circle
• Standard form of a circle

References

• Math Open Reference
• Khan Academy

Frequently Asked Questions

• Q: What is the equation of a circle in standard form? A: The equation of a circle in standard form is ${(x-h)^2 + (y-k)^2 = r^2}$.
• Q: How do you identify the center of a circle given its equation? A: To identify the center of a circle, you need to look at the values of ${h}$ and ${k}$ in the equation.
• Q: What are the values of ${h}$ and ${k}$ in the equation of a circle? A: The values of ${h}$ and ${k}$ represent the x-coordinate and y-coordinate of the center of the circle, respectively.
  Circle Equation Q&A: Understanding the Basics =====================================================

Introduction

In mathematics, a circle is a set of points that are all equidistant from a central point known as the center. The equation of a circle in standard form is given by ${(x-h)^2 + (y-k)^2 = r^2}$, where ${(h, k)}$ represents the coordinates of the center of the circle, and ${r}$ is the radius. In this article, we will answer some frequently asked questions about the equation of a circle.

Q&A

Q: What is the equation of a circle in standard form?

A: The equation of a circle in standard form is ${(x-h)^2 + (y-k)^2 = r^2}$. This equation represents a circle with center ${(h, k)}$ and radius ${r}$.

Q: How do you identify the center of a circle given its equation?

A: To identify the center of a circle, you need to look at the values of ${h}$ and ${k}$ in the equation. The values of ${h}$ and ${k}$ represent the x-coordinate and y-coordinate of the center of the circle, respectively.

Q: What are the values of ${h}$ and ${k}$ in the equation of a circle?

A: The values of ${h}$ and ${k}$ represent the x-coordinate and y-coordinate of the center of the circle, respectively. For example, in the equation ${(x-2)^2 + (y-3)^2 = 4}$, the center of the circle is ${(2, 3)}$.

Q: How do you find the radius of a circle given its equation?

A: To find the radius of a circle, you need to look at the value of ${r^2}$ in the equation. The radius of the circle is the square root of ${r^2}$. For example, in the equation ${(x-2)^2 + (y-3)^2 = 4}$, the radius of the circle is ${\sqrt{4} = 2}$.

Q: What is the difference between the equation of a circle and the equation of an ellipse?

A: The equation of a circle is given by ${(x-h)^2 + (y-k)^2 = r^2}$, while the equation of an ellipse is given by ${\frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{b^2} = 1}$. The main difference between the two equations is that the equation of a circle has the same value for ${a}$ and ${b}$, while the equation of an ellipse has different values for ${a}$ and ${b}$.

Q: How do you graph a circle given its equation?

A: To graph a circle, you need to plot the center of the circle and then draw a circle with the given radius. You can use a compass to draw the circle.

Q: What are some real-world applications of the equation of a circle?

A: The equation of a circle has many real-world applications, including:

• Designing circular shapes in architecture and engineering
• Calculating the area and circumference of a circle
• Modeling the motion of objects in physics and engineering
• Analyzing data in statistics and data analysis

Conclusion

In conclusion, the equation of a circle is a fundamental concept in mathematics that has many real-world applications. By understanding the basics of the equation of a circle, you can solve problems and analyze data in a variety of fields.

Related Topics

• Equation of an ellipse
• Graphing a circle
• Real-world applications of the equation of a circle

References

• Math Open Reference
• Khan Academy

Frequently Asked Questions

• Q: What is the equation of a circle in standard form? A: The equation of a circle in standard form is ${(x-h)^2 + (y-k)^2 = r^2}$.
• Q: How do you identify the center of a circle given its equation? A: To identify the center of a circle, you need to look at the values of ${h}$ and ${k}$ in the equation.
• Q: What are the values of ${h}$ and ${k}$ in the equation of a circle? A: The values of ${h}$ and ${k}$ represent the x-coordinate and y-coordinate of the center of the circle, respectively.