Take an element $p \notin (x, y)$. You can always represent it this way $p = xf + yg+ h$ where $f, g\in\mathbb{Q}[x,y], h \in \mathbb{Q}$.  Then it follows that $h \neq 0$ since $p \notin (x, y)$. Then $h$, which is invertible is in $(x, y, p)$, which means that $(x, y, p) = (1)$. Then $(x, y)$ is maximal because the only ideal which strictly contains it is $(1)$. 

Maximal ideal in $\mathbb{Q}[x,y]$
How to read Exif data from Image.
There is ExifLib but have problem with Lumia device and Data taken field.
Are there any other way to read Exif data on Windows Phone (7./8).

Best regards
