## Saturday, June 25, 2011

### Parabola

A parabola has a standard equation of

$(x-h)^2=4p(y-k)$ ------(1)

or

$(y-k)^2=4p(x-h)$ ------(2)

where (h,k) is the coordinate of the vertex (labeled as V in the graph).

For the parabola of type (1), the parabola is either opening upwards (p > 0) or downwards(p < 0). This type of parabola has a focus at F(h, k + p) and a directrix at y = k - p.

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On the other hand, for the parabola of type (2), the parabola is either opening rightwards (p > 0) or leftwards(p < 0). This type of parabola has a focus at F(h + p, k) and a directrix at x = h - p.

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