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keisanHigh-precision calculations for everyday life and work

Determine the parabola from three points (perpendicular to the axis)

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Determine the parabola from three points.
Assume the axis of the parabola is vertical (parallel to the y-axis).
The equation of the parabola is in the form y = ax² + bx + c.
Here, results where a = 0 are allowed.
Also output results that are straight lines.
Enter three datasets without duplicates. (If there are duplicates, nothing will be output.)
If the data consists of coordinates, enter three points.
If a parabola can be determined, it will be output. (Limited to finite values.)
The output will be a, b, and c.
x1
y1
x2
y2
x3
y3
Was a decision made or not?   Decision made = 0, No = 1
a   Coefficient of the x^2 term
b   Coefficient of the x-term
c   Constant term
R6 (2024). September 15 (Sun)_Ver. 001
Digit setting: 50 digits. Digit count can be changed. Complex number calculation mode.

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