Explanation

(a)
Let us assume the equation of parabola whose axis is parallel to $y$-axis and touch $x$-axis.
$y = ax^{2} + bx + c$ ...(i)
and $b^{2} = 4ac\ \ \ (\because$ curve touches $x$-axis)
$\because$ There are two arbitrary constant.
$\therefore$ Order of this equation is 2.