Lab for Determinants and Conic Section Curves

Exercise 7.  Use the determinant method to find the standard ellipse through the points (6,1), (2,2), (1,4), (9,2).

Solution 7.  The points are entered into Mathematica with the command:

Then a row vector corresponding to equation (9) is defined:

The matrix A for the linear system in (10) and the determinant is now created.  The vector R is stored in the first row by issuing the command  A = {R}.  Then the remaining five rows of A are generated with the loop command:

For the given three points, the homogeneous system AC = 0 is:

The determinant of this matrix is computed by typing:

This quantity is multiplied by   to get the desired equation:

The conic is the circle shown in Figure 7.  It is plotted using the commands:

(c) John H. Mathews