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(2): An asymptotic view (spoiler) by Harry)

For b = a and P in quadrant (45,135).

Let Q be the foot of the perpendicular from P to asymptote=45. If the ray from P is parallel to asymptote=45, then the distance from the ray to the branch of the hyperbola in quadrant (-45,45) is greater than |PQ|.

Seems a strange definition for a tangent line. But, it's a thoughtful point.

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Bye the way, I liked your proof of the original problem. My proof started with a point on the curve and derived one of the other two points on the curve such that lines tangent to the curve at the starting point and the derived point are orthognal. Your proof took about a third of a page where mine took three to four pages.

Edited on November 27, 2011, 1:59 am

Posted by Bractals on 2011-11-27 01:48:06