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

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.

Answer 1

[Torsten]

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.

[Shree]

Thank you so much!

Answer 2

[Star Strider]

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.

[John D'Errico]

And it takes 3 DISTINCT points to define a parabola. :) +1 anyway

[Shree]

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?