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(3): An asymptotic view (spoiler)
Yes, I see what you mean Bractals, but I'm not claiming that this parallel line is a tangent to the hyperbola. I quite agree that from that point P there isn't a tangent to that 'edge' of the hyperbola.
However, for a=b, if you take the line through P parallel to theta=45 and reduce its gradient by any amount it will cross the hyperbola and can't therefore be a limiting ray for the viewing angle. So that parallel line would be seen by an observer at P as the limiting ray (assuming they could see to infinity).
Edited on November 27, 2011, 3:30 pm
Posted by Harry
on 2011-11-27 15:29:45