anonymous
  • anonymous
Find the equation of the parabola given the focus (2,-3) and the directrix is x=8
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
what i did was
anonymous
  • anonymous
|dw:1446439914460:dw|
anonymous
  • anonymous
|dw:1446439979740:dw|

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triciaal
  • triciaal
|dw:1446447003469:dw|
anonymous
  • anonymous
so i got \[(y+3)^2=4p(x-5)\]\[(y+3)^2=-12(x-5)\]
anonymous
  • anonymous
is that correct?
triciaal
  • triciaal
@campbell_st
anonymous
  • anonymous
@campbell_st is offline
triciaal
  • triciaal
y = (x-5)^2 -3
anonymous
  • anonymous
how did you get that?
anonymous
  • anonymous
o i see
triciaal
  • triciaal
|dw:1446447547572:dw|
anonymous
  • anonymous
so whats the value of "a"
triciaal
  • triciaal
is it 3?
anonymous
  • anonymous
im not sure im custom with p... not a ..i dont know what "a" but i know p is the distance from the focus to the vertex ... is it the same for "a"?
triciaal
  • triciaal
I forgot what to substitute in the equation using a point to get a
anonymous
  • anonymous
ok
anonymous
  • anonymous
thanks for your help im going to bed now
campbell_st
  • campbell_st
the parabola is in the form \[(y-k)^2 = -4a(x - h)\] the parabola is concave left, hence the negative... so find the distance from the focus to the directrix.. this will be 2a then its a case of just substituting.
campbell_st
  • campbell_st
the vertex is be a units to the right of the focus... on the line y = -3 so the distance focus to directrix is 6 units..... so a =3 then the vertex is at (2 +3, -3) or (5, -3) so the parabola is \[(y + 3)^2 = -4 \times 3 \times (x - 5)\] so you are correct @Alilnn
triciaal
  • triciaal
thanks @campbell_st

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