Are you struggling to find the radius of a circle whose equation is given? Don’t worry! In this article, we will explain how to find the radius of a circle when its equation is given. The equation of a circle is given in the standard form (x – h)² + (y – k)² = r², where (h, k) is the center of the circle and r is the radius. In this case, we are given the equation x² + y² – 10x + 6y + 18 = 0.

## Introduction

The radius of a circle is an essential part of the circle. It is the distance from the center of the circle to any point on its circumference. Knowing the radius of a circle is crucial in solving various problems in geometry, physics, engineering, and many other fields. In this article, we will learn how to find the radius of a circle when its equation is given.

## Understanding the Circle Equation

The equation of a circle in the standard form is (x – h)² + (y – k)² = r². This equation tells us that the distance from any point (x, y) on the circle to the center (h, k) is equal to the radius (r). When the equation of a circle is given in a different form, we need to convert it to the standard form to find the center and radius.

## Finding the Radius of a Circle

To find the radius of a circle whose equation is given, we need to first convert the equation to the standard form. Let’s take the given equation x² + y² – 10x + 6y + 18 = 0 and complete the square for x and y.

x² – 10x + y² + 6y + 18 = 0 (x² – 10x + 25) + (y² + 6y + 9) = 25 – 9 – 18 (x – 5)² + (y + 3)² = 1

Now we have the equation in the standard form (x – h)² + (y – k)² = r², where (h, k) is the center of the circle and r is the radius. Therefore, the center of the circle is (5, -3), and the radius is 1 unit.

## FAQs

### Q1. What is the equation of a circle in the standard form?

A. The equation of a circle in the standard form is (x – h)² + (y – k)² = r², where (h, k) is the center of the circle and r is the radius.

### Q2. How do you find the center of a circle from its equation?

A. To find the center of a circle from its equation, we need to convert the equation to the standard form (x – h)² + (y – k)² = r² and then identify the values of (h, k).

### Q3. What is the radius of a circle?

A. The radius of a circle is the distance from the center of the circle to any point on its circumference.

### Q4. Can a circle have a negative radius?

A. No, a circle cannot have a negative radius. The radius is always a positive number.

### Q5. How is the radius of a circle related to its diameter?

A. The radius of a circle is half the length of its diameter.

The radius of a circle is an important property because it tells us how far each point on the circle is from the center. This has many applications in the real world, such as finding the distance between two objects or determining the size of a circular object.

## Conclusion:

In conclusion, the radius of the circle with equation x2+y2+8x-6y+21=0 is 2 units. The process of finding the radius involved completing the square for both x and y terms and transforming the equation into the standard form. Understanding the equation of a circle and its properties is important in many fields, including mathematics, engineering, and physics.