Guten Morgen,

there are 3 (one-parameter) families which passes through the vertices of this square:

1. ellipses

2. hyperbolae opening to the right and the left

3. hyperbolae opening up and down

The center of all conics is the origin.

to #1.: The general equation of an ellipse with center at (0, 0) and the axes a and b is:

..........Plug in the coordinates of (-1, 1) and (1, 1):

.......... Plug in this term for bē into the original equation of the ellipse:

Don't forget to calculate the domain of the family!

To demonstrate the effect of this equation I've attached a drawing with 1 < a < 5

To #2, #3: Use the same method.