Page 106 - Calc for the Clueless

Here we must complete the square in a slightly different manner.

Center: (5,-3). Vertices: . . Foci:

Of course you should use 5 instead of . I leave the so you know where it came from.

The definition of the hyperbola is F 1P - PF 2 = 2a, where the foci are (±c,0). The derivation is exactly the same as
2
2
2
2
for an ellipse. Once is enough!! The equation we get is x /a - y /b = 1, where a + b = c are called the
2
2
transverse vertices. The hyperbola has asymptotes y = ±(b/a)x.
Note 1
The shape of a hyperbola is determined by the location of the minus sign, not which number is larger under the
x or y .
2
2