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Homework Statement
My book gives the theorem for parabolas as:
The graph of the equation:
[tex] y = ax^{2} [/tex]
(where [tex] a \neq 0 [/tex] ) is the parabola with focus [tex] F(0,\frac{1}{4}a) [/tex] and the directrix [tex] y = -(\frac{1}{4}a)[/tex]. Its vertex is [tex] (0,0) [/tex], and its axis is the y-axis.
It then goes on to use these equations in an example like so:
PROOF: Let us find the equation of the parabola with focus F(0,d) and directrix y= -d.
Where [tex] d= \frac{1}{4}a [/tex]
*Rest of proof omitted as it has nothing to do with what I am asking*
so then it moves on to an example where it asks:
Find the focus and directrix of the parabola:
[tex] y = -\frac{1}{2}x^{2} [/tex]
*straight from the book*=
Using Theorem 1 (the theorem posted above):
[tex] a = -\frac{1}{2} \;\;\;\; and \;\;\;\; d= \frac{1}{4}a [/tex]
so in this problem:
[tex] d = -\frac{1}{2} [/tex] ?
_________________________________
*End from book*
Shouldn't d = -1/8 not -1/2? If d = (1/4)a and a = -1/2, then isn't (-1/2)(1/4) = -1/8?
I ask this only because every other point in this chapter builds from this point and I want to make sure I am not just stupid and there is actually a problem here.
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