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:
- Choose Beginning Calculus from the initial menu and press
.
- Use the arrow keys to move to the menu item Graph F(x,y)=c, press
and
.
- At the prompt F(x,y) =, enter the formula
x y
- and use the bounds
- x0 = -3 x1 = 3
- y0 = -3 y1 = 3
- At the prompt, N = , enter 8
and
- 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
|
- You will then see the graphs of eight hyperbolas.
- Press .
- Use the arrow keys to move to Superimpose and press
.
- At the prompt, F(x,y)=, type in
x^2 - y^2 .
- At the prompt, N=, just enter 8
and
- 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
|
- You will then see the following:
