Problem:
Plot the graphs of the family of hyperbolas

x y = c

together with the graphs of the orthogonal family of hyperbolas

x2 - y2 = c


Visualization:
Using Microcalc:

  1. Choose Beginning Calculus from the initial menu and press .
  2. Use the arrow keys to move to the menu item Graph F(x,y)=c, press and .
  3. At the prompt F(x,y) =, enter the formula
    x y
  4. and use the bounds
    x0 = -3 x1 = 3
    y0 = -3 y1 = 3
  5. At the prompt, N = , enter 8 and
  6. at each of the following prompts, enter
    c_1 = 1 c_2 = 2
    c_3 = 3 c_4= 4
    c_5 = -1 c_6 = -2
    c_7 = -3 c_8= -4
  7. You will then see the graphs of eight hyperbolas.

  8. Press .
  9. Use the arrow keys to move to Superimpose and press .
  10. At the prompt, F(x,y)=, type in x^2 - y^2 .
  11. At the prompt, N=, just enter 8 and
  12. at each of the following prompts, enter
    c_1 = 1 c_2 = 2
    c_3 = 3 c_4= 4
    c_5 = -1 c_6 = -2
    c_7 = -3 c_8= -4
  13. You will then see the following: