Foot of perpendicular from one end of latus rectum L(3, 4) on major axis which is focus is given by
$\frac{\mathrm{x}-3}{1}=\frac{\mathrm{y}-4}{-2}=\frac{-(3-2(4)-5)}{1^2+(-2{)}^2}=2$
$\therefore \mathrm{S}(\mathrm{x},\mathrm{y})\equiv \mathrm{S}(5,0)$
Another focus is image of s in the line 2x + y + 10 = 0.
$\begin{array}{l}\frac{\mathrm{x}-5}{2}=\frac{\mathrm{y}-0}{1}=\frac{-2\left(2\right(5)+0+10)}{2^2+1^2}=-8\\ \therefore {\mathrm{S}}^{\mathrm{\prime }}(\mathrm{x},\mathrm{y})\equiv \mathrm{S}(-11,-8)\end{array}$