anonymous
  • anonymous
Parabola Help. Write 3y^2+24y+72x-96=0 in standard form. I got (y+4)^2=-24(x-2) is that right? also what is the focus? line of symmetry? Directrix?
Mathematics
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chestercat
  • chestercat
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jim_thompson5910
  • jim_thompson5910
you are correct 3y^2+24y+72x-96=0 is equivalent to (y+4)^2=-24(x-2)
jim_thompson5910
  • jim_thompson5910
(y+4)^2=-24(x-2) (y-(-4))^2=-24(x-2) (y-(-4))^2=-4(6)(x-2) the equation is now in the form (y-k)^2 = -4p(x-h) where in this case h = 2 k =-4 p = 6 this means that 1) the parabola opens in a horizontal direction, either left or right because of the y^2 term 2) the parabola opens up to the left (since we have a negative -4 on the right side, if it was positive, then it would open up to the right) 3) the value of p determines how far the focus is from the vertex and it determines how far the directrix is from the vertex 4) the focus lies on the axis of symmetry
anonymous
  • anonymous
got it thanks! @jim_thompson5910

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jim_thompson5910
  • jim_thompson5910
tell me what you got for the focus and directrix
jim_thompson5910
  • jim_thompson5910
oh and forgot to mention that (h,k) is the vertex, but I'm sure you know that already
anonymous
  • anonymous
I got (-4,-4) and 8. vertex:(2,-4) of coarse.
jim_thompson5910
  • jim_thompson5910
(-4,-4) is the focus, good x = 8 for the directrix (2,-4) is the vertex all 3 are correct
anonymous
  • anonymous
yahoo! (:
jim_thompson5910
  • jim_thompson5910
lol nice work

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