Given the equation x2
/9 + y2
/4 = 1 find the set of all points from which the angle of view*
of this ellipse is a right angle. What is the significance of this set of points?
Given the equation x2/9 - y2/4 = 1 find the set of all points from which the angle of view* of this hyperbola is a right angle. What is the significance of this set of points?
* i.e. displaying a right angle between the two tangents.
(In reply to re: An asymptotic view (spoiler)
Just the origin? Can we go further when b = a?
If a curve with an asymptote is viewed from a point P on the other side of the asymptote then the limiting ray for the angle of view of the curve is the line drawn from P to the point of infinity on the asymptote. That means the ray is parallel to the asymptote. I think that would be the reality for a person with infinitely good visibility.
Now, if itís a rectangular hyperbola (b=a) then I believe that from any point P in the quadrant 135<theta<225, the branch of the curve lying in the
vertically opposite quadrant, -45<theta<45, will have an angle of view of 90 degrees, since the two limiting rays through P, parallel to the two perpendicular asymptotes, will themselves be perpendicular (and v.v.).
Posted by Harry
on 2011-11-26 18:14:33