Respuesta :
Answer: The required center of the given circle is 2 units.
Step-by-step explanation: We are given to find the radius of a circle with the following equation:
[tex]x^2+y^2+8x-6y+21=0~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
The standard equation of a CIRCLE with radius 'r' units and center at the point (h, k) is given by
[tex](x-h)^2+(y-k)^2=r^2.[/tex]
From equation (i), we have
[tex]x^2+y^2+8x-6y+21=0\\\\\Rightarrow (x^2+8x+16)+(y^2-6y+9)-16-9+21=0\\\\\Rightarrow (x^2+2\times x\times 4+4^2)+(y^2-2\times x\times 3+3^2)-4=0\\\\\Rightarrow (x+4)^2+(y-3)^2=4\\\\\Rightarrow (x-(-4))^2+(y-3)^2=2^2.[/tex]
Comparing the above equation with the standard equation (i), we get
radius, r = 2 units and center, (h, k) = (-4, 3).
Thus, the required center of the given circle is 2 units.
