Question

Find vertex and focus for the equation $y^2-8y-x+19=0$

Answer 1

$\begin{array}{c}{y}^2-8y-x+19=0\\ y^2-2\left(4\right)y+16+3=x\\ {\left(y-4\right)}^2=\left(x-3\right)\left[\begin{array}{c}{y}^2=4ax\\ A=\frac{1}{4}\end{array}\right]\\ y=y-4\\ x=x-3\\ x=3\\ y=4\\ vertex=\left(3,4\right)\\ focus:\\ x-3=\frac{1}{4}\\ x=\frac{13}{4}\\ y=4\end{array}$