Plotting Implicit Functions

Examples 1-7 are plotted using the x domain -10x10 with autoscaling on (checked).

Example 1: Elliptic Curves

• Plot e1(x,y): y^2 = x^3-7x+6

  

• Plot e2(x,y): y^2 = x^3-2x+4

  

Example 2: Families of Implicit Curves

• Plot e4(x,y): x^2 +3x y +y^3 = c

  

Example 3: Conic Sections -- An Ellipse

• Plot e5(x,y): x^2/49 + y^2/9 = 1

  

Example 4: Folium of Descartes

• Plot e6(x,y): x^3+y^3 = 6x y

  Note: You can not plot an object in the Work window unless it has a checkmark to its left. If the object does not have a checkmark, click in the position where the checkmark should be and one will be drawn. At most, five objects can have checkmarks at the same time.

  

Example 5: Conchoid of Nicomedes

• Plot e7(x,y): x^2 y^2 = (y+1)^2 (4-y^2)

  

Example 6: Estimating the Solutions to a System of Nonlinear Equations

• Plot e8(x,y): x^2+2y^3 = 15
• Overlay a plot of e9(x,y): x^4-y^2 = 7x

  

Example 7: Orthogonal Trajectories

• Plot e10(x,y): y = a x^3
• Overlay a plot of e11(x,y): x^2 + 3y^2 = b

  

Example 8: Optical Illusions

• Change the x plotting domain in the Domain & Range window to -3x3.
• Plot e12(x,y):
• Click the Line Segment tool on the Tool Palette.
• Click in the Domain & Range window to make it the active window.
• Type -2 into the "x1 =" cell and 1 into the "y1 =" cell.
• Click the Enter button.
• Type 2 into the "x2 =" cell and 1 into the "y2 =" cell.
• Click the Enter button.
• Click the Enter button again.
• Type 2 into the "x2 =" cell and -1 into the "y2 =" cell.
• Click the Enter button.
• Click the Enter button again.
• Type -2 into the "x2 =" cell and -1 into the "y2 =" cell.
• Click the Enter button.
• Click the Enter button again.
• Type -2 into the "x2 =" cell and 1 into the "y2 =" cell.
• Click the Enter button.

  You should have drawn four line segments forming a rectangle. Note how it appears that the lines are bending in.

  

Copyright 2000-2008 Adam O. Hausknecht and Robert E. Kowalczyk