Plot the graphs of the family of hyperbolas

together with the graphs of the orthogonal family of hyperbolas

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 formulax 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: