The parameter a occurs in the standard equations y2=4ax and x2=4ay.
(i) Explain the geometric meaning of the quantity a with reference to the vertex and the focus of the parabola.
(ii) Describe how the sign of a influences the orientation (opening direction) of each standard form, supporting your explanation with suitable examples.
(iii) For the equation y2=4ax with a=−5, state the focus, directrix, axis, and length of the latus rectum, and comment on their positions relative to the coordinate axes.