Page 80 - Calculus for the Clueless, Calc II

The definition of the hyperbola is F 1P - PF 2 = 2a where the foci are (±c,0). The derivation is exactly the same as
for an ellipse. Once is enough!! The equation we get is x /a - y /b = 1, where a + b = c . The coordinates
2
2
2
2
2
2
2
(±a,0) are called the 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
2
2
x or y .
Note 2
In the case of the asymptote, the slope of the line b/a is the square root of the number under the y divided by
2
the square root of the term under the x term.
2
Example 10—

Sketch and label x /7 - y /11 = 1.
2
2
Transverse vertices, y = 0, ,. Note that if x = 0, , which is imaginary. The curve
does not hit the y-axis; ; foci are ; and .