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Flauer [41]
3 years ago
8

How can the equation of a parabola be derived when given the focus and the directrix?

Mathematics
1 answer:
pickupchik [31]3 years ago
4 0
The distance between any point (x0,y0) on the parabola and the focus (m,n) is the same as the distance between (x0,y0) and the directrix line ax+by+c. The distance between (x0,y0) and focus (a,b) is \sqrt((x-m)^2+(y-n)^2). The distance between (x0,y0) and ax+by+c is |ax0+by0+c|/\sqrt(m^2+n^2).  Equalize these two expressions.
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