The focus of parabola whose vertex is (4,5) and whose equation of directrix is $\mathrm{x}+\mathrm{y}+1=0$ is

$$\begin{gathered} \mathrm{Vertex}\left(A\right)=\left(4,5\right) and \mathrm{directrix} is \mathrm{x}+\mathrm{y}+1=0 \\ \mathrm{Let} Z\left(\mathrm{h}, \mathrm{k}\right) \mathrm{is} \mathrm{the} \mathrm{foot} \mathrm{of} \mathrm{the} perpendicular \mathrm{from} vertex \mathrm{to} \mathrm{directrix} \\ \frac{\mathrm{h}-4}{1}=\frac{\mathrm{k}-5}{1}=\frac{-\left(4+5+1\right)}{2} \end{gathered}$$

$$\begin{gathered} \mathrm{h}-4=\mathrm{k}-5=-5 \\ \mathrm{h}=-1, \mathrm{k}=0 \\ Z=\left(\mathrm{h}, \mathrm{k}\right)=\left(-1,0\right) \end{gathered}$$

$$\begin{gathered} \mathrm{Vertex}\left(A\right)=\frac{\mathrm{S}+Z}{2} \\ 2A=\mathrm{S}+Z \\ \mathrm{S}=2A-Z \\ \mathrm{S}=\left(8+1, 10-0\right)=(9, 10) \end{gathered}$$