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Re: geometry help
Posted:
Apr 24, 2014 10:21 AM
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> Hello, can you please help me to resolve the
> following?
>
> 1) If points Z1 and Z2 are known, what is the minimum
> number of additional points we need to know in order
> to define a parabola?
> 2) What will be the formula to describe the parabola
> using Y and X two-dimensional plane?
> 3) What will be the formula to calculate value of M1
> and M2?
Dear kelvin m,
>From your figure you are dealing with a parabola with an axis of symmetry parallel to the y-axis, so it will be of the form
y=a.x^2 + b.x + c
so you need 3 points to fully determine it, but they can't all be in a straight line otherwise the parabola will be degenerate.
>From point Z1(0,4) we get c=4
>From point Z2(80,0) we get 0=a.80^2 + b.80 + 4 ...(1)
Let's assume the third point is Z3(40,8)
It doesn't have to have its x-value midway between Z1 and Z2, but from your figure its y-value should be greater than 5 for 0<x<80
Then Z3 gives 8=a.40^2 + b.40 + 4 ...(2)
Solve (1) and (2) for a and b and we get
y = -(3/800).x^2 +(1/4).x + 4
To get M1 and M2 find the y values of the parabola for the two given x values and compare to y=5
Regards, Peter Scales.
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