How many ways can 6 people be chosen and arranged in a straight line if there are 8 people to choose from? 720 20,160 40,320 48?
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The line is called the directrix. Here we have a vertical directrix, so a parabola sideways from usual.
Geometry is best done with squared distances. The squared distance from an arbitrary point (x,y) to the vertical line x=2 is
We equate that to the squared distance of (x,y) to the focus (-2,0):
We could call that done. A more standard form might be
Geometry is best done with squared distances. The squared distance from an arbitrary point (x,y) to the vertical line x=2 is
We equate that to the squared distance of (x,y) to the focus (-2,0):
We could call that done. A more standard form might be