I currently have an expression of an Hyperboloid equation :
Where a,b,c,d are some real constants.
I would like to know what is the best way to transform it into the standard Hyperboloid, i.e
(which can be written as v.Av=1 considering v=(x,y,z))
I was thinking of putting u=(u1,u2,u3), so we have to transform u in v, i.e we have to find some P invertible matrix, and a u0 ( shift ) so we have u=Pv+u0 and then we can identify to my equation
but this method requires so many variables, i have a system with way too many variables (12, 9 from the matrix and 3 form the shift) and i can obtain only 10 equations from identification, so i have to choose some coefficients.
Is there a better way to find this matrix P and this u0 / an other way of considerating things?
Thanks again, and sorry for my bad english