Answer:
Center: (2,-1)
Radius: 4 units
Step-by-step explanation:
Equation of the circle in standard form is:
[tex]x^{2}+y^{2}+2gx+2fy+c=0[/tex]
The radius of this circle is located at (-g, -f) and its radius is equal to:
[tex]r=\sqrt{g^{2}+f^{2}-c}[/tex]
The given equation of circle is:
[tex]x^{2}+y^{2}-4x+2y-11=0[/tex]
Re-writing this equation in a form similar to the standard equation:
[tex]x^{2}+y^{2}+2(-2)x+2(1)y-11=0[/tex]
Comparing this equation with standard equation we can say:
g= -2
f = 1
c = -11
So, the center of the circle will be located at (-g, -f) = (2, -1)
And the radius will be = [tex]\sqrt{g^{2}+f^{2}-c} =\sqrt{(-2)^{2}+(1)^{2}-(-11)} =\sqrt{16} =4[/tex]
Thus the radius of the given circle is 4 units.
