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# Find an equation of the parabola that has a focus at (9,7) and a vertex at (9,2)?

y= (x-9)^2+2 is not the right answer

### 3 Answers

- Anonymous1 decade agoFavorite Answer
You've got to find the directrix line first. Then a point on the parabola is one that is equidistant from the focus and the directrix.

The directrix is always perpendicular to the line passing through the focus and the vertex, and it lies at the same distance from the vertex as the focus does. So, in this case, the directrix is the line y = -3 (draw a diagram). The square of the dist of a point (x, y) from this line is just (y+3)^2. So the equal-dist condition for (x, y) to be on the parabola is

(x-9)^2 + (y-7)^2 = (y+3)^2

which expands to

y = (1/20)(x-9)^2 + 2.

- 1 decade ago
The equation would be y= (1/20)(x-9)^2 +(1/10). The equation for an up-facing parabola is 4a(y-y0)=(x-x0)^2 where a is the distance from the focus to the vertex (5, since 7-2=5).

- Anonymous1 decade ago
I found a site that easily explains what you are trying to find:

http://home.alltel.net/okrebs/page64.html

Guido