We define a tangent line to a hyperbola as a line that is not parallel to an asymptote
Chapter 11, Problem 56(choose chapter or problem)
We define a tangent line to a hyperbola as a line that is not parallel to an asymptote and that intersects the hyperbolain exactly one point. Show that the equation of the linetangent to the hyperbola x2/a2 y2/b2 1 at the point(x1, y1) on the curve isHint: Allow for signs, but follow exactly the same steps aswere supplied in Exercise 61 of Exercise Set 11.4, wherewe found the tangent to the ellipse. You should find thatthe slope in the present case is m (b2x1/a2y1). Explainwhy this slope cannot equal the slope of an asymptote aslong as (x1, y1) is on the hyperbola.
Unfortunately, we don't have that question answered yet. But you can get it answered in just 5 hours by Logging in or Becoming a subscriber.
Becoming a subscriber
Or look for another answer