First we need to convert the given equation of circle to its standard form, only then we can calculate its center and radius.
[tex] x^{2} +y^{2} +14x-10y+65=0 \\ \\
x^{2} +2(x)(7)+ y^{2}-2(y)(5)=-65 \\ \\
x^{2} +2(x)(7)+ (7)^{2}+ [y^{2}-2(y)(5)+ (5)^{2}]=-65+(7)^{2}+(5)^{2} \\ \\
(x+7)^{2}+(y-5)^{2}=9 [/tex]
The above equation is in standard form.
The center of the circle is (-7, 5) and its radius is 3.
