Find the standard form of the equation of the parabola with a focus at (0, -9) and a directrix y = 9.

Question

anonymous · Answer

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

anonymous · Answer

4p?

campbell_st · Answer

1st the directrix is above the focus... so the parabola is concave down. 

next the distance between the focus and directrix is twice the focal length... a

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the focal length a = 9. 

the vertex is a units above the focus

so the vertex is (0, -9 + 9)

so the vertex of the parabola is at (0,0)

so using the vertex form where (h, k) is the vertex and a is the focal length

$$(x - h)^2 = 4a(y - k)$$

substituting you get 

$$(x - 0)2 = 4 \times 9 (y - 0)$$

or

$$x^2 = 36y$$

yo get it into standard from just make y the subject. 

hope it helps