Answer
The equation represents a circle
$ (x-2)^2+(y^2+5)^2=4^2$
with center $(2,-5)$ and radius is $4$
Work Step by Step
$\underline{\textbf{Given equation}}$
$x^2+y^2-4x+10y+13=0$
$\Rightarrow x^2+y^2-4x+10y=-13$
$\Rightarrow x^2-4x+y^2+10y=-13$
$\Rightarrow (x^2-4x)+(y^2+10y)=-13$
$\Rightarrow (x^2-4x+4)+(y^2+10y+25)=-13+4+25$
$\Rightarrow (x-2)^2+(y^2+5)^2=16$
$\Rightarrow (x-2)^2+(y^2+5)^2=4^2$
Which is the standard form for the equation of circle with center $(2,-5)$ and radius is $4$
