How to draw parabola given two points A(x1,y1) & B(x2,y2)?

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Shree
Shree 2015-3-5
评论： Shree 2015-3-5
Hello, I need to draw the parabola and I have two points First: A(1.2643, 5.6106) Last: B(120, 45).
I have tried varies formulas but the graph is not correct. Specially some formulas assume b=0 in the general parabola formula y = ax^2 + bx + c but in my case it is not zero.
Please tell me how to do it for this specific example.

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采纳的回答

Torsten
Torsten 2015-3-5
Parabola: p(x)=ax^2+bx+c
tan(50°)=p'(x1)=2*a*1.2643+b
5.6106=p(x1)=a*1.2643^2+b*1.2643+c
45=p(x2)=a*120^2+b*120+c
This is a linear system of equations in a,b,c and can be solved by
x=[2*1.2643 1 0; 1.2643^2 1.2643 1; 120^2 120 1]\[tand(50);5.6106;45]; %x(1)=a, x(2)=b, x(3)=c
Best wishes
Torsten.

更多回答（1 个）

Star Strider
Star Strider 2015-3-5
Two points can define a line, but you need at least three to uniquely describe a parabola.
Infinitely many parabolas can be drawn through only two points.
  2 个评论
John D'Errico
John D'Errico 2015-3-5
编辑：John D'Errico 2015-3-5
And it takes 3 DISTINCT points to define a parabola. :) +1 anyway
Shree
Shree 2015-3-5
I have angle of 50 deg at the starting point with reference to x axis(from tangent of parabola), will that help to get the parabola. Is there any way to do it with these three inputs?

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