The radius of a circle is a measure of its size, and is determined by its equation. In this article, we will discuss how to calculate the radius of a circle whose equation is given as x2+y2+8x−6y+21=0.
What is the Radius of a Circle?
The radius of a circle is the distance from the center of the circle to any point on the circle. It is the same for all points on the circle, and is equal to half of the diameter of the circle. The radius is an important concept in geometry, and is used to calculate the area and circumference of a circle.
Solving the Equation x2+y2+8x−6y+21=0
To calculate the radius of a circle whose equation is given as x2+y2+8x−6y+21=0, we first need to solve the equation. To do this, we can use the quadratic equation. This equation can be written as a2+bx+c=0, where a, b, and c are constants. In this case, a=1, b=8, and c=-6.
Using the quadratic equation, we can solve for x and y. The solutions are x= -4 and y=3. This means that the center of the circle is at (-4,3). To calculate the radius, we simply need to calculate the distance between the center of the circle and any point on the circle.
For example, if we choose the point (1,1) as our point on the circle, the distance between the two points can be calculated using the Pythagorean theorem. This distance is equal to the radius of the circle. In this case, the radius is equal to 5.
In conclusion, the radius of a circle whose equation is given as x2+y2+8x−6y+21=0 can be calculated by solving the equation using the quadratic equation, and then calculating the distance between the center of the circle and any point on the circle. In this example, the radius of the circle is 5.
Finding the radius of a circle can be a tricky task if you are not familiar with some basic principles of mathematics. Fortunately, this article will explain how to calculate the radius of a circle whose equation is given as x2+y2+8x−6y+21=0.
In order to solve for the radius, we must first look at the equation. The equation that we are given is in the form of a general conic equation, which is defined as a second-degree equation in two variables (x and y) that defines a conic section. This equation can be written in the standard form as (x – h)2 + (y – k)2 = r2, where h and k represent the x and y coordinates of the circle’s center and r is the radius of the circle.
Now that we know how to write the equation in standard form, we can solve for the radius of the circle. We start by substituting the general second-degree equation into the standard form and then solving for the radius. After substituting the equation and solving for r2, we get the following: r2 = (−4)2 + (3)2 = 25. The square root of this number gives us the radius of the circle, which is 5 units.
In conclusion, the radius of a circle whose equation is given as x2+y2+8x−6y+21=0 is 5 units. This result can be obtained by substituting the equation into the standard form for circles and then solving for the radius.
