Find the pair of tangent from (4, 10) to the circle ${\mathrm{x}}^2+{\mathrm{y}}^2=25$

Given circle is $\mathrm{s}={\mathrm{x}}^2+{\mathrm{y}}^2-25=0$
Equation to pair of tangent from (4, 10) to s = 0 is ${\mathrm{SS}}_{11}={\mathrm{s}}_1^2$
$\begin{array}{l}\Rightarrow \left({\mathrm{x}}^2+{\mathrm{y}}^2-25\right)(16+100-25)=[4\mathrm{x}+10\mathrm{y}-25{]}^2\\ 91\left({\mathrm{x}}^2+{\mathrm{y}}^2-25\right)=16{\mathrm{x}}^2+100{\mathrm{y}}^2+625+80\mathrm{xy}-500\mathrm{y}-200\mathrm{x}\\ \Rightarrow 75{\mathrm{x}}^2-9{\mathrm{y}}^2-80\mathrm{xy}+200\mathrm{x}+500\mathrm{y}-2900=0\end{array}$