LevelCurvesConics
Author: Mike May, S.J.
Date: February 27, 2009

Applet lets you look at level curves of a general quadratic equation

It was created by Marc Renault

a*x^2+b*y^2+c*x*y+d*x+e*y=k

u = 0.34 (slider from 0 to 1, step 0.01)
dx: x(Corner[2.0] - Corner[1.0]) / 100.0
dy: y(Corner[4.0] - Corner[1.0]) / 100.0
Δk = 1 (slider from 0.25 to 5, step 0.25)
a = 1 (slider from -5 to 5, step 0.1)
b = -0.9 (slider from -5 to 5, step 0.1)
c = 0 (slider from -5 to 5, step 0.1)
d = 0 (slider from -5 to 5, step 0.1)
e = 0 (slider from -5 to 5, step 0.1)
k_{min} = -25 (slider from -25 to 0, step 0.1)
k_{max} = 25 (slider from 0 to 25, step 0.1)
k: k_{min} + (k_{max} - k_{min}) u
LevelCurvesPos = Sequence(myConic[a, b, c, d, e, k], k, Δk, k_{max}, Δk)
D: (x(Corner[1.0]) + 20.0 dx, y(Corner[4.0]))
A = Corner(4.0)
B: (x(Corner[1.0]), y(Corner[1.0]) + 50.0 dy)
C: (x(D), y(B))
poly1, a_1, b_1, c_1, d_1 = Polygon(A, B, C, D)
con: a 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 x^(2.0) + b 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 y^(2.0) + c 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 x 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 y + d 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 x + e 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 y = k
txtKval: "k = " + k
LevelCurvesNeg = Sequence(myConic[a, b, c, d, e, k], k, k_{min}, -1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 Δk, Δk)
LevelCurvesZero = myConic(a, b, c, d, e, 0.0)
txtConicEqn: "" + (myConic[a, b, c, d, e, k])
Cor1 = Corner(1.0)
poly2, f, g, h, i = Polygon(Cor1, Cor1 + (0.0, 12.0 dy), Cor1 + (48.0 dx, 12.0 dy), Cor1 + (48.0 dx, 0.0))

Tool: myConic
a, b, c, d, e, k
Input: a, b, c, d, e, k
Output: con

con: a 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 x^(2.0) + b 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 y^(2.0) + c 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 x 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 y + d 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 x + e 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 y = k