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| Math Central | Quandaries & Queries |
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Question from srujana, a student: Can we find the equation of the parabola when only two points on it are known and neither of them is the focus nor the vertex? |
Srujana,
The general form of a parabola is y = a x2 + b x + c where a, b and c are constants. If you know three points on the parabola you can use them to generate 3 linear equations in the variables a, b and c which you can then solve to determine the equation. If you only know two points then this is not enough information to determine the equation, you need another piece of information. If for example you know that the parabola is symmetric about the y-axis then b = 0 and the 2 points will allow you to determine a and c.
I hope this helps,
Harley
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