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Please help understanding what the question is asking Calc II (Conics)

  1. May 6, 2012 #1
    1. The problem statement, all variables and given/known data

    Find an equation is standard form for the conic that satisfies the given condition.
    Parabola: vertex (2,3), vertical axis passing through (1,5)
    2. Relevant equations
    vertex= (h,k)


    3. The attempt at a solution

    I know how to solve a problem like this if I was given the vertex and/or any combination of focus, directrix, p, etc. What is confusing me about this problem is "vertical axis passing through 1,5". In all of my HW problems I have never encountered a problem in which this was given as information to find the equation. I do not know what it has to do with the problem or how that information allows me to continue on.
    Any help on what relevance that has for this problem/ equations relevant to that to allow me to work this out would be very much appreciated, thank you.
     
  2. jcsd
  3. May 7, 2012 #2

    sharks

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    Gold Member

    The axis of symmetry in standard form is the line: [itex]x=-\frac{b}{2a}[/itex]
     
  4. May 7, 2012 #3
    Thank your reply. However, I do not think that equation is relevant to this problem. This being because the only information I am given is the vertex aside from that. The vertex is in the form (h,k). Other than that x is given to me if the "vertical axis" is actually the "vertically axis of symmetry" and we would then have 1=-b/2a. Perhaps I do not have enough mathematical knowledge to solve for b and a given only x in that equation and if that is the case could you please show me how you would do so. Thank you.
     
  5. May 7, 2012 #4

    sharks

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    Draw the graph and attach it to your reply. You'll notice that it isn't "typical" where the axis of symmetry is parallel to the x-axis or y-axis.
     
  6. May 7, 2012 #5

    HallsofIvy

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    What you are given, if it actually uses the word "vertical", is impossible. The vertical line through (1, 5) has equation x= 1. The vertex of the parabola must lie on that axis but (2, 3) does not. It might well be that the "axis of symmetry" is NOT vertical (so that word should not be used) but is the line through (2, 3) and (1, 5), y= -2(x-2)+ 3= -2x+ 7. However, knowing only that and the vertex is still not enough to determine the conic section. There exist an infinite number of parabolas havinng a given axis of symmetry and vertex, having different foci.
     
  7. May 7, 2012 #6

    Ray Vickson

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    As written the problem is self-contradictory. However, if you replace the words "vertical axis" by "symmetry axis" the problem makes sense; it is asking about a slanted parabola that is tilted away from vertical orientation. Then there are infinitely many possible candidates, because the supplied information is not enough to determine a unique parabola; just make yourself a rough sketch to understand why.

    RGV
     
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