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 Angle of view - Ellipse and Hyperbola (Posted on 2011-11-24)
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.

 No Solution Yet Submitted by Jer Rating: 4.0000 (1 votes)

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 Solution - Proof upon request. | Comment 1 of 7

For the curve
x^2         y^2
----- + s * ----- = 1,
a^2         b^2
the circle
x^2 + y^2 = a^2 + s * b^2
is the locus of points with
an angle of view of 90 degrees.
Where s = +1 for an ellipse and
s = -1 for a hyperbola.
This was discovered with a
combination of algebra and
Note: The four points (a,b), (-a,b),
(-a,-b), and (a,-b) are
clearly members of the locus
for the ellipse.
Note: For the hyperbola - if b >= a,
then there are no points with
an angle of view of 90 degrees.

 Posted by Bractals on 2011-11-24 14:28:58

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