Answer:
Center: (-9, -2)
Radius = 6
Step-by-step explanation:
The general equation of the circle is:
[tex]x^{2} + y^{2}+2gx+2fy+c=0[/tex]
The center of the circle is given as (-g, -f) and the radius of this circle is calculated as:
[tex]r=\sqrt{g^{2}+f^{2}-c}[/tex]
The given equation is:
[tex]x^{2} +y^{2}+18x+4y+49=0[/tex]
Re-writing this equation in a form similar to general form:
[tex]x^{2} +y^{2}+2(9)(x)+2(2)(y)+49=0[/tex]
Comparing this equation with general equation we get:
g = 9
f = 2
c = 49
Thus center of the given circle is (-g, -f) = (-9, -2)
The radius of the circle will be:
[tex]r=\sqrt{9^{2}+2^{2}-49}=6[/tex]
Thus the radius of the given circle is 6.
