Equation for parabola with focus
- Thread starter TonyC
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- Apr 12, 2005
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Not really. That has to be something squared in there, or you won't get a parabola.
The vertex is a very helpful clue. It is usually named (h,k) and we are given h = -5 and k = -4. This gives two possibilities:
y-k = r*(x-h)<sup>2</sup> ==> y+4 = r*(x+5)<sup>2</sup>
x-h = r*(y-k)<sup>2</sup> ==> x+5 = r*(y+4)<sup>2</sup>
The focus gives a couple of clues. One is the basic orientation of the parabola. In this case, the foxus is directly above the vertex, so it is a parabola that opens up. It ALWAYS opens in the same direction as travelling from the vertex to the focus. We are down to this.
y+4 = r*(x+5)<sup>2</sup>
More from the focus. Another is the distance, usually called p/2. It is the distance from the vertex to the focus. Pretty obviously, we have p/2 = 5, making p = 10. There should be a formula somewhere in your materials showing that r = 1/(2*p). This makes r = 1/20.
y+4 = (1/20)*(x+5)<sup>2</sup>
Or, if you like,
20*(y+4) = (x+5)<sup>2</sup>
The vertex is a very helpful clue. It is usually named (h,k) and we are given h = -5 and k = -4. This gives two possibilities:
y-k = r*(x-h)<sup>2</sup> ==> y+4 = r*(x+5)<sup>2</sup>
x-h = r*(y-k)<sup>2</sup> ==> x+5 = r*(y+4)<sup>2</sup>
The focus gives a couple of clues. One is the basic orientation of the parabola. In this case, the foxus is directly above the vertex, so it is a parabola that opens up. It ALWAYS opens in the same direction as travelling from the vertex to the focus. We are down to this.
y+4 = r*(x+5)<sup>2</sup>
More from the focus. Another is the distance, usually called p/2. It is the distance from the vertex to the focus. Pretty obviously, we have p/2 = 5, making p = 10. There should be a formula somewhere in your materials showing that r = 1/(2*p). This makes r = 1/20.
y+4 = (1/20)*(x+5)<sup>2</sup>
Or, if you like,
20*(y+4) = (x+5)<sup>2</sup>
