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4x^2 = 7y How do they get the following for the focus and directix?

  1. Oct 6, 2011 #1
    Please don't leave out very many steps, please do give the formulas if possible please thank you:
    How did they get these values?
    Focus = (0,7/16)
    directrix = -7/16

    Tried to use p=1/4(a) which DID NOT work , that yields p = 1
    THEN the focus would be (0,1) which it is not. Teacher said to use that formula but maybe that was for who knows what , because it's not working.
  2. jcsd
  3. Oct 6, 2011 #2
    [itex]4x^2=7y \rightarrow 4x^2+0x+0=7y \rightarrow (4/7)x^2+0x+0=y[/itex]
    thus, the focus is
    (-\frac{0}{2\cdot(\frac{4}{7})}, -\frac{0^2}{4\cdot(\frac{4}{7})}+0+\frac{1}{4\frac{4}{7}} ) = ( 0, \frac{7}{16} )
    the same thing goes with the directrix.

    hope it helped.
    Last edited: Oct 6, 2011
  4. Oct 6, 2011 #3


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    Homework Helper

    ^No offense, but I don't know how that post could have helped. It was hard for me to read.

    You are not applying the formula correctly. One of the equations of the parabola is
    x2 = 4py,
    but your equation is
    4x2 = 7y.
    You have a coefficient for the x2 term. So the first thing you must do is to divide both sides by 4.
    [itex]x^2 = \frac{7}{4}y[/itex]
    Now you can figure out the focus and directrix.
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