The area of the circle $x^2+y^2-4x-2y+k=0$ is $25\pi$ square units then k =

The given circle is $x^2+y^2-4x-2y+k=0$

Radius of the abvoe circle is 

    $\begin{array}{rcl}r& =& \sqrt{g^2+f^2-c}\\ & =& \sqrt{4+1-k}\\ & =& \sqrt{5-k}\end{array}$

The area of the circle is $25\pi$ square units

Hence, ${\mathrm{\pi r}}^2=25\mathrm{\pi }$

$\begin{array}{rcl}5-k& =& 25\Rightarrow k=\boxed{\mathbf{-}\mathbf{20}}\end{array}$