What Is The Radius Of A Circle Whose Equation Is { (x+5) 2+(y-3) 2=4^2$}$?A. 2 Units B. 4 Units C. 8 Units D. 16 Units

Understanding the Equation of a Circle

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 of the circle. In the given equation ${(x+5)^2 + (y-3)^2 = 4^2}$, we can identify the center of the circle as ${(-5, 3)}$ and the radius as ${r}$.

Identifying the Radius of the Circle

To find the radius of the circle, we need to take the square root of the value on the right-hand side of the equation, which is ${4^2}$. This is because the radius is the square root of the square of the distance from the center to any point on the circle.

Calculating the Radius

The value on the right-hand side of the equation is ${4^2}$, which is equal to ${16}$. Therefore, the radius of the circle is the square root of ${16}$, which is ${\sqrt{16} = 4}$.

Conclusion

Based on the given equation of the circle, we have found that the radius of the circle is ${4}$ units.

Comparison with the Given Options

The options given are A. 2 units, B. 4 units, C. 8 units, and D. 16 units. Based on our calculation, the correct answer is B. 4 units.

Final Answer

The final answer is B. 4 units.

Additional Information

The equation of a circle can be written in the form ${(x-h)^2 + (y-k)^2 = r^2}$, where ${(h,k)}$ is the center of the circle and ${r}$ is the radius. The radius is the distance from the center to any point on the circle. In this case, the center of the circle is ${(-5, 3)}$ and the radius is ${4}$ units.

Example Use Case

To find the radius of a circle, we can use the equation of the circle in standard form. For example, if the equation of the circle is ${(x-2)^2 + (y+1)^2 = 9}$, we can identify the center of the circle as ${(2, -1)}$ and the radius as ${\sqrt{9} = 3}$.

Common Mistakes

One common mistake when finding the radius of a circle is to forget to take the square root of the value on the right-hand side of the equation. This can lead to an incorrect answer.

Tips and Tricks

To find the radius of a circle, make sure to identify the center of the circle and the value on the right-hand side of the equation. Then, take the square root of the value on the right-hand side to find the radius.

Conclusion

In conclusion, the radius of a circle whose equation is ${(x+5)^2 + (y-3)^2 = 4^2}$ is ${4}$ units. This can be found by identifying the center of the circle and the value on the right-hand side of the equation, and then taking the square root of the value on the right-hand side.

Q: What is the radius of a circle in the equation ${(x+5)^2 + (y-3)^2 = 4^2}$?

A: The radius of the circle is 4 units.

Q: How do I find the radius of a circle?

A: To find the radius of a circle, you need to identify the center of the circle and the value on the right-hand side of the equation. Then, take the square root of the value on the right-hand side to find the radius.

Q: What is the center of the circle in the equation ${(x+5)^2 + (y-3)^2 = 4^2}$?

A: The center of the circle is (-5, 3).

Q: What is the value on the right-hand side of the equation ${(x+5)^2 + (y-3)^2 = 4^2}$?

A: The value on the right-hand side of the equation is 4^2, which is equal to 16.

Q: Why do I need to take the square root of the value on the right-hand side of the equation?

A: You need to take the square root of the value on the right-hand side of the equation because the radius is the square root of the square of the distance from the center to any point on the circle.

Q: What is the square root of 16?

A: The square root of 16 is 4.

Q: What is the radius of a circle in the equation ${(x-2)^2 + (y+1)^2 = 9}$?

A: The radius of the circle is 3 units.

Q: How do I identify the center of a circle in an equation?

A: To identify the center of a circle in an equation, you need to look for the values of x and y that are being subtracted from x and y, respectively. In the equation ${(x-2)^2 + (y+1)^2 = 9}$, the center of the circle is (2, -1).

Q: What is the value on the right-hand side of the equation ${(x-2)^2 + (y+1)^2 = 9}$?

A: The value on the right-hand side of the equation is 9.

Q: Why do I need to take the square root of the value on the right-hand side of the equation?

A: You need to take the square root of the value on the right-hand side of the equation because the radius is the square root of the square of the distance from the center to any point on the circle.

Q: What is the square root of 9?

A: The square root of 9 is 3.

Q: What is the radius of a circle in the equation ${(x+5)^2 + (y-3)^2 = 25}$?

A: The radius of the circle is 5 units.

Q: How do I find the radius of a circle?

A: To find the radius of a circle, you need to identify the center of the circle and the value on the right-hand side of the equation. Then, take the square root of the value on the right-hand side to find the radius.

Q: What is the center of the circle in the equation ${(x+5)^2 + (y-3)^2 = 25}$?

A: The center of the circle is (-5, 3).

Q: What is the value on the right-hand side of the equation ${(x+5)^2 + (y-3)^2 = 25}$?

A: The value on the right-hand side of the equation is 25.

Q: Why do I need to take the square root of the value on the right-hand side of the equation?

A: You need to take the square root of the value on the right-hand side of the equation because the radius is the square root of the square of the distance from the center to any point on the circle.

Q: What is the square root of 25?

A: The square root of 25 is 5.

Conclusion

In conclusion, the radius of a circle can be found by identifying the center of the circle and the value on the right-hand side of the equation, and then taking the square root of the value on the right-hand side. The center of the circle is the values of x and y that are being subtracted from x and y, respectively, and the value on the right-hand side of the equation is the square of the distance from the center to any point on the circle.