(1) Find an equation that represents a hyperbola on which the closest points to the origin are (-4,0) and (4,0) and which has asymptotic lines y = 3x and y = -3x.
SOLUTION:
Since the asymptotic lines are 3x and -3x, this shows they meet at the point (0,0).
(x - 0)2 (y - 0)2
-------- - -------- = 1
a2 b2
b/a = 3 ==> b = 3a
Let a = 1 (you can choose any number here)
Then the equation becomes:
x2 - y2/9 = 1