13Feb/11Off
Focus Formula
Focus Formula
How to find the standard equation of a parabola with given focus point and directrix?
focus (3,5)
directrix y=-1
use a distance formula to find the vertex first, am i right?
The vertex is halfway between the focus and directrix. Since there are six units distance, minimum, from y=-1 to (3,5)...
... the focal distance is 3, half of six... that is how far is the vertex from both the focus and the directrix...
vertex(3,2)
Therefore... the vertex form of the parabola will be:
y = a(x - 3)² + 2
The problem is finding a, the specific shape of the parabola.
In all parabolas... d = 1/(4a)... where 'd' is the focal distance
3 = 1/(4a)
a = 1/12
So, our parabola is
y = (1/12)(x - 3)² + 2
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