# What is the equation in standard form of the parabola with a focus at (14,15) and a directrix of y= -7?

The equation of parabola is

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The equation in standard form of the parabola with a focus at (14,15) and a directrix of y= -7 is:

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

where (h, k) is the vertex of the parabola and p is the distance between the vertex and the focus (or the vertex and the directrix).

Given the focus (14,15) and the directrix y= -7:

- The vertex is halfway between the focus and the directrix, so the vertex is (14, 4).
- The distance between the focus and the vertex is the same as the distance between the directrix and the vertex, which is 15 - (-7) = 22.
- Since the parabola opens upward, p = 22.

Plugging in the values: (x - 14)^2 = 4 * 22(y - 4)

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