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

Question

Shree 2015-3-5

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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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Answer 1

Torsten 2015-3-5

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在 MATLAB Online 中打开

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.

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Shree 2015-3-5

Thank you so much!

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Answer 2

Star Strider 2015-3-5

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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.

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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 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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