Respuesta :
The radius of the circle of the provided equation, after comparing it with the standard equation of the circle, is 2.
What is the equation of circle?
The equation of the circle is the equation which is used to represent the circle in the algebraic equation form with the value of center point in the coordinate plane and measure of radius.
The standard form of the equation of the circle can be given as,
[tex](x-h)^2+(y-k)^2=r^2[/tex]
Here (h,k) is the center of the circle and (r) is the radius of the circle.
The given equation of the circle is,
[tex]x^2+ y^2 +8x-6y +21=0[/tex]
Add number 16 and 9 both sides of the equation to complete the square.
[tex]x^2+ y^2 +8x-6y +21+16+9=16+9\\x^2+8x+16+ y^2 -6y +9=16+9-21\\(x+4)^2+(y-3)^2=4\\(x+4)^2+(y-3)^2=2^2[/tex]
Compare it with the standard equation of the circle, we get,
[tex]h=-4\\k=3\\r=2[/tex]
Hence, the radius of the circle of the provided equation, after comparing it with the standard equation of the circle, is 2.
Learn more about the equation of circle here;
https://brainly.com/question/1506955
