The radius of a circle is an important parameter when it comes to understanding the shape and size of a circle. In this article, we’ll discuss how to calculate the radius of a circle given the equation x2+y2+8x−6y+21=0.
Calculating the Radius of a Circle
The radius of a circle can be calculated by using its equation. A circle is a closed two-dimensional shape with a curved line as its circumference. The equation of a circle is x2+y2+8x−6y+21=0. The equation can be used to calculate the radius of the circle by solving the equation for the radius.
Solving the Equation x2+y2+8x−6y+21=0
To solve for the radius, first, the equation must be rearranged. The equation can be rearranged to the form x2+y2+ax+by+c=0, where a, b, and c are constants. In this case, a=8, b=-6, and c=21.
The radius can be calculated by using the formula r=√(a2+b2-4ac)/2a. In this case, a=8, b=-6, and c=21. Substituting these values into the formula, we get r=√(82+(-6)2-4821)/2*8 = √(64+36-672)/16 = √(-568)/16 = 5 units.
Therefore, the radius of the circle whose equation is x2+y2+8x−6y+21=0 is 5 units.
In conclusion, the radius of a circle can be calculated using its equation. In this article, we discussed how to calculate the radius of a circle given the equation x2+y2+8x−6y+21=0. We solved the equation and found that the radius of the circle is 5 units.