Alex Astashyn A function that returns the polynomial of degree n - 1 which passes through the n points in matrix mat . The matrix of points is an n x 2 matrix where the n th row consists of the x and y coordinates of the n th point. The programs must all be placed in the same folder. The equation may be in any form, but the variables must be x and y . Upon execution, the program will present a menu of output choices.
Points returns a matrix of information describing the conic.
Center, Vertices, Foci, Directrix, Asymptotes, and Orientation of the primary axis are given as appropriate. Try it with parabolas, ellipses, hyperbolas, and degenerate conics. If the conic does not have it's axis parallel to either the x or y axes the program transforms the variables and writes a new equation in new variables x' and y' . The new equation is a conic that does have its axis aligned with one of the coordinate axes. This transformed conic has the shape of the original conic but has been rotated by an angle so that it may be recognized in one of the three standard forms above.