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The length of latus -rectum of the parabola $x^{2}+2 y=8 x-7$ is
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2
We have,
$\begin{array}{l}
x^{2}+2 y=8 x-7 \\
x^{2}-8 x=-2 y-7 \\
x^{2}-8 x+16=-2 y-7+16 \\
(x-4)^{2}=-2 y+9 \\
(x-4)^{2}=-2(y-9 / 2)
\end{array}$
$\therefore$ Length of latus rectum $=2$
$\begin{array}{l}
x^{2}+2 y=8 x-7 \\
x^{2}-8 x=-2 y-7 \\
x^{2}-8 x+16=-2 y-7+16 \\
(x-4)^{2}=-2 y+9 \\
(x-4)^{2}=-2(y-9 / 2)
\end{array}$
$\therefore$ Length of latus rectum $=2$
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