$\displaystyle \begin{array}{{>{\displaystyle}l}} \mathrm{Gọi\ \Delta :2x+y+c=0.}\\ \mathrm{Gọi\ M( 0;3) \in d}\\ \mathrm{Do\ d//\Delta }\\ \mathrm{nên\ ta\ có:\ d( M,\Delta ) =\frac{|2.0+3+c|}{\sqrt{2^{2} +1^{2}}} =5}\\ \mathrm{\Leftrightarrow |c+3|=5\sqrt{5}}\\ \mathrm{\Leftrightarrow c=5\sqrt{5} -3\ \ or\ c=-5\sqrt{5} -3}\\ \mathrm{Vậy\ \Delta :2x+y+5\sqrt{5} -3\ =0.\ hoặc\ 2x+y-5\sqrt{5} -3\ =0} \end{array}$
