We derived the standard parabola but I keep forgetting where the focus sits and what the directrix line is. Can someone explain it clearly?
For the standard parabola y² = 4ax (opening to the right with vertex at the origin), the focus is the point (a, 0) on the positive x-axis, and the directrix is the vertical line x = −a. The number a is the distance from the vertex to the focus, and also from the vertex to the directrix, so the vertex sits exactly halfway between them. The defining property is that every point on the parabola is equidistant from the focus and the directrix. The length of the latus rectum, the chord through the focus perpendicular to the axis, is 4a. If the equation were y² = −4ax it opens left with focus (−a, 0) and directrix x = a. Always identify a first by comparing your equation to y² = 4ax.
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