Calculating the radius of a circle with a given equation may seem like a daunting task, but it is actually quite simple. In this article, we will discuss how to calculate the radius of a circle whose equation is x2+y2+8x−6y+21=0, and determine which of the given units is the most appropriate.
Calculating the Radius of a Circle
The equation of a circle is usually written in the form (x−h)2+(y−k)2=r2, where (h, k) is the center of the circle, and r is the radius. To calculate the radius of the circle given in the equation x2+y2+8x−6y+21=0, we can manipulate the equation into the form (x−h)2+(y−k)2=r2.
First, we can move all terms with x to the left side of the equation and all terms with y to the right side of the equation. This gives us x2−8x+y2−6y=−21. Then, we can add 4 to both sides and factor out the x and y terms to get (x−4)2+(y−3)2=25.
We can now identify the center of the circle as (4, 3) and the radius as 5.
Determining the Appropriate Units
The equation does not specify which units are used for the radius, so it is important to determine the unit of measurement before calculating the radius. In this case, the given units are 2, 3, 4, and 5. Of these options, the correct unit is 5, since the radius of the circle is 5.
In conclusion, the radius of a circle whose equation is x2+y2+8x−6y+21=0 is 5 units. Knowing how to calculate the radius of a circle with a given equation is a valuable skill that can be used in a wide range of applications.
