in reply to Re^4: OT:Math problem: Grids and conical sections.
in thread OT:Math problem: Grids and conical sections.

There appears to be an error in your calculations or transcription of them.

Specifically, the sign of the 

y2
 component of equation 1, changes between the original form 
    (x-1)2 + y2 = m(z - h1)2
___________^

and it's expansion: 

    x2 - 2x + 1 - y2 = m(z2 - 2zh1 + h12)
________________^

I don't follow the steps you used in the next stage of the reduction, (Eq.2 - Eq.1)/m, so I am unable to filter the correction through the rest of the workings.

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Re^6: OT:Math problem: Grids and conical sections.
by tilly (Archbishop) on Nov 28, 2005 at 16:31 UTC
    The error was in my transcription. That sign error was irrelevant because, no matter what I typed, I knew that the squares cancelled out.

    Your trouble following the next step was due to another typo, 4 instead of 2. The idea goes like this: 

    Eqn 2 - Eqn 1:

  (x2 + y2 - 2y + 1)
    - (x2 - 2x + 1 + y2)
      = m(z2 - 2zh2 + h22)
        - m(z2 - 2zh1 + h12)

  -2y + 2x
    = m(- 2zh2 + h22 + 2zh1 - h12)
    Now divide both sides by m. Do the same for the other equation.
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