Lab for Determinants and Conic Section Curves

Module for Conic Curve Fit

Background.  Five points in the plane uniquely determine an equation for a conic section. The implicit formula for a conic section is often mentioned in textbooks, and the special cases for an ellipse, hyperbola, parabola, circle are obtained by either setting some coefficients equal to zero or making them the same value, etc.
Load in Mathematica's graphics packages "Colors" and "ImplicitPlot".

Implicit equation for a line.

Exercise 1.  Use the determinant method to find the line through the points (1,4) and {5,3).

Solution 1.

Exercise 2.  Use the determinant method to find the line through the points  (3,1) and (3,4).

Solution 2.

Exercise 3.  Use the determinant method to find the line through the points  (1,4) and (5,4).

Solution 3.

Implicit equation for a circle.

Exercise 4.  Use the determinant method to find the circle through the points (6,1),  (2,2)  and  (1,4).
Remark. In Exercises 5 and 6 the same points are used to find the standard parabola and alternate parabola.

Solution 4.

Implicit equations for parabolas.

Exercise 5.  Use the determinant method to find the standard equation of a parabola through the points (6,1),  (2,2)  and  (1,4).
Remark. In Exercises 4 and 6 the same points are used to find the circle and alternate parabola.

Solution 5.

Exercise 6.  Use the determinant method to find the alternate equation of a parabola through the points (6,1),  (2,2)  and  (1,4).
Remark. In Exercises 4 and 5 the same points are used to find the circle and standard parabola.

Solution 6.

Implicit equation for a standard ellipse.

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 implicit equation for a 5 point conic.

Exercise 8.  Determine the conic that passes through the five points  .  

Solution 8.

Exercise 9.  Determine the conic that passes through the five points .  

Solution 9.

Exercise 10.  Determine the conic that passes through the five points   .  

Solution 10.

Exercise 11.  Determine the conic that passes through the five points  .  

Solution 11.

Exercise 12.  Determine the conic that passes through the five points .  

Solution 12.

(c) John H. Mathews