Problem 96AE

Approach to asymptotes Show that the vertical distance between a hyperbola x2/a2 − y2/b2 = 1 and its asymptote y = bx/a approaches zero as x → ∞, where 0<b<a.

Solution 96AE

Step 1:

To find

Show that the vertical distance between a hyperbola x2/a2 − y2/b2 = 1 and its asymptote y = bx/a approaches zero as x → ∞, where 0<b<a.