itsmichelle29
  • itsmichelle29
I give medals to helpers thanks Regan is trying to find the equation of a quadratic that has a focus of (−2, 5) and a directrix of y = 13. Describe to Regan your preferred method for deriving the equation. Make sure you use Regan's situation as a model to help her understand.
Mathematics
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SOLVED
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katieb
  • katieb
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itsmichelle29
  • itsmichelle29
can you guys help me plz
anonymous
  • anonymous
y = -1/16(x - (-2))^2 +9.
itsmichelle29
  • itsmichelle29
I dont understand

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More answers

itsmichelle29
  • itsmichelle29
Describe to Regan your preferred method for deriving the equation. Make sure you use Regan's situation as a model to help her understand. Can you give me this answer
misty1212
  • misty1212
HI!!
itsmichelle29
  • itsmichelle29
hi omg can you please help me
misty1212
  • misty1212
no one likes these conic section questions, but they are not that hard really
misty1212
  • misty1212
first off, do you know what the parabola would look like (open right, left, up or down?)
itsmichelle29
  • itsmichelle29
Nope
misty1212
  • misty1212
hmm that is a problem lets plot the focus and graph the directrix
itsmichelle29
  • itsmichelle29
okay
misty1212
  • misty1212
|dw:1434503255264:dw|
misty1212
  • misty1212
you can see that the focus \((-2,5)\) is BELOW the directrix, which is a horizontal line that means the parabola will open DOWN
itsmichelle29
  • itsmichelle29
Ohhh okay
misty1212
  • misty1212
the next thing we need to do is find the vertex do you know how to find it ?
itsmichelle29
  • itsmichelle29
No ='(
misty1212
  • misty1212
it is the point half way between \((-2,5)\) and \(y=13\) what is half way between \(5\) and \(13\)?
itsmichelle29
  • itsmichelle29
9
misty1212
  • misty1212
right (got logged out somehow)
misty1212
  • misty1212
that means the vertex is \((-2,9)\)
misty1212
  • misty1212
now we are almost done
itsmichelle29
  • itsmichelle29
OKAY
itsmichelle29
  • itsmichelle29
so now what ?
misty1212
  • misty1212
since the vertex is \((-2,5)\) and it opens down, it will look like \[4p(y-9)=(x+2)^2\] all we need is \(p\) and to note that \(4p\) will be negative since it opens down
misty1212
  • misty1212
oops i meant "since the vertex is \((-2,9)\) my mistake
itsmichelle29
  • itsmichelle29
no its -2 5
misty1212
  • misty1212
to find \(p\) is also easy it is the distance between the focus \((-2,5)\) and the vertex \((-2,9)\)
itsmichelle29
  • itsmichelle29
ohhh n.m.
misty1212
  • misty1212
how far from \(5\) to \(9\)?
misty1212
  • misty1212
did i lose you?

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