Jesus said: *"Y = aX 2 + bX + c." His disciples wondered: "We don't always understand what you say, but this is particularly cryptic!" Jesus replied: "Of course—it is a parabola."*
Everyone knows the parabola! But given its axis, a point P and its tangent ( T ) at P, we do not always know how to construct the parabola's focus and directrix with straightedge and compass.
Here is a short guide for geometric emergencies.
Focus, sweet focus……
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The tangent ( T ) to the parabola at P intersects the parabola's axis at A.
