The radius of a circle with the given equation is 5 units.
Given the following data:
- [tex]x^2+y^2+8x-6y+21=0[/tex]
The equation of a circle.
Mathematically, the standard form of the equation of a circle is given by;
[tex](x-h)^2+(y-k)^2=r^2[/tex]
Where;
- h and k represents the coordinates at the center.
- r represents the radius of the circle.
Expanding the equation, we have:
[tex]x^2+y^2-2hx-2ky+(h^2+k^2-r^2)=0\\\\r=\sqrt{h^2+k^2}[/tex]
Comparing the terms, we have:
-2hx = 8x
h = -4
-2ky = -6y
k = 3.
For the radius:
[tex]r=\sqrt{-4^2+3^2}\\\\r=\sqrt{16+9} \\\\r=\sqrt{25}[/tex]
r = 5 units.
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