To answer this, use "completing the square."
x2 + y2 + 8x – 6y + 21 = 0 becomes
x^2 + 8x + 16 - 16 + y^2 - 6y + 9 - 9 + 21 = 0
(x + 4)^2 -16 + (y - 3)^2 + 12 = 0
or (x + 4)^2 + (y - 3)^2 = 4
Since 4 = r^2, r = 2 units, and the center is at (-4, 3)
The radius of a circle whose general form of the equation is given as x^2 + y^2 + 8x – 6y + 21 = 0 would be 2 units.
The general equation of a circle of radius r represents all the points that lie on the circumference of the given circle.
The general equation of a circle is:
[tex]\rm x^2 + y^2 + 2gx + 2fy + c = 0[/tex]
The given general equation of a circle
[tex]\rm x^2 + y^2 + 8x - 6y + 21 = 0[/tex]
by completing the square method, we get
[tex]\rm x^2 + 8x + 16 - 16 + y^2 - 6y + 9 - 9 + 21 = 0[/tex]
[tex](x + 4)^2 -16 + (y - 3)^2 + 12 = 0[/tex]
[tex](x + 4)^2 + (y - 3)^2 = 4[/tex]
Thus 4 = r^2, r = 2 units,
Learn more about the general equation of a circle:
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