How to get equation of a curve plotted using( z=ax^2+by^2).

Can anyone tell me a method by which i could get back the bi-quadratic equation using which i have generated data points for the curve z=a.x^2+b.y^2.Please guide me

Answer 1

[Roger Stafford]

Assuming you have generated the data points accurately, you need only two data points (x1,y1,z1) and (x2,y2,z2) to retrieve your a and b coefficients. Just solve the two simultaneous linear equations in a and b, x1*a+y1*b=z1 and x2*a+y2*b=z2:

[x1,y1;x2,y2]\[z1;z2];

The result should be [a;b].

[Note: It strikes me as curious that you could so easily lose those two coefficients after making use of them for generating the data.]