anonymous
  • anonymous
.
Algebra
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
please explain too.
welshfella
  • welshfella
take any point on the parabola (x0,y0) then the distance between this point and the focus is given by sqrt[(x0 - 2)^2 + (y0 - 0)^2 and distance of the point from the directrix = 12
welshfella
  • welshfella
- sorry that distance from directrix is |y0 - 12|

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welshfella
  • welshfella
so as the distance from the focus = distance from the directrix ( definition of a parabola) we have sqrt[(x0 - 2)^2 + (y0 - 0)^2 = (0 -12) simplify this to get the required equation
welshfella
  • welshfella
sorry - another typo its sqrt[(x - 2)^2 + (y - 0)^2] = (y -12)
welshfella
  • welshfella
- I change x0 and y0 to x and y
welshfella
  • welshfella
squaring both sides (x - 2)^2 + y^2 = (y - 12)^2 x^2 - 4x + 3 + y^2 = y^2 - 24y + 144 can you continue from here?
anonymous
  • anonymous
Could you go all the way please?
anonymous
  • anonymous
gave you best response
welshfella
  • welshfella
x^2 - 4x + 4 + y^2 = y^2 - 24y + 144 x^2 - 4x - 140 = -24y y = (-1/24)x^2 + (1/6)x - 35/6 = 0
anonymous
  • anonymous
thanks.
welshfella
  • welshfella
I'm making a lot of typos today so I cant guarantee the answer but the method is right!
anonymous
  • anonymous
yeah its an answer could you help me with one more
welshfella
  • welshfella
no sorry gtg right now
welshfella
  • welshfella
I'm still not happy with that result
anonymous
  • anonymous
what result?
welshfella
  • welshfella
AH! the distance for directrix is |x - (-12)| = |x + 12| so we have (x - 2)^2 + y^2 = y^2 + 24x + 144 x^2 - 4x + 4 + y^2 = y^2 + 24y + 144 x^2 - 4x - 144 + 4 = 24x y = (1/24)x^2 - (1/6)x - 144/24 = 0 y = (1/24)x^2 - (1/6)x - 35/6 = 0 is the correct answer
welshfella
  • welshfella
the only problem with that is its not one of the options but I'm sure its correct
welshfella
  • welshfella
I'll check with wolfram alpha
anonymous
  • anonymous
lol wolfram
welshfella
  • welshfella
http://www.wolframalpha.com/input/?i=equation+of+a+parabola+with+focus+%282%2C0%29+and+directrix+y+%3D+-12 there you go its correct
anonymous
  • anonymous
okay
welshfella
  • welshfella
so there must be a typo in one of the choices looks like its C - which has 2 plus instead 2 negatives

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