# How To Plot A Curve With Given Three Points?

by optics.tech
Tags: curve, plot, points
 P: 80 Hi everyone, Can someone please tell me is there any mathematical equation/formula on ploting a curve with given three coordinates/points such as below image? Thank you very much for your help Op Attached Thumbnails
 HW Helper P: 930 There are infinitely many curves you can draw through three points. The simplest method it to use a 2nd order polynomial (i.e a parabola). Just write out 3 equations using the values of x & y: y1 = a x21 + b x1+ c y2 = a x22 + b x2+ c y3 = a x23 + b x3+ c This is 3 equations in 3 unknowns (a,b,c) that can be solved by substitution.
 Sci Advisor P: 2,751 As hotvette has already said, there are infinitely many curves you can draw through three points. Two common cases in which the curve is uniquely specified by three points are the parabola and the circle. That is, if you assume it's a circle then such a circle is unique, and if you assume it's a parabola then such a parabola is unique.
P: 743

## How To Plot A Curve With Given Three Points?

 if you assume it's a parabola then such a parabola is unique
No, there are an infinity of parabolas that can be draw through three points, each one with a different axial direction. Of course, il you asume a given direction for the axis, the parabola is unique.
P: 80
 There are infinitely many curves you can draw through three points. The simplest method it to use a 2nd order polynomial (i.e a parabola). Just write out 3 equations using the values of x & y: y1 = a x21 + b x1+ c y2 = a x22 + b x2+ c y3 = a x23 + b x3+ c This is 3 equations in 3 unknowns (a,b,c) that can be solved by substitution.
What about if the amount of the points are nine pieces?

Will above equations can be continued from three to nine equations with similar pattern?

Does this curve is a kind of smooth and continue curve?