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What is the area of the triangle formed by the the asymptote of a hyperbola and any tangent to the hyperbola

What is the area of the triangle formed by the the asymptote of a hyperbola and any tangent to the hyperbola

Grade:12

2 Answers

Vijay Mukati
askIITians Faculty 2590 Points
5 years ago
Dear Student,
Hint:
Find the two points of intersections of tangents with the asymptotes to get the two vertexes.
And third vertex is the centre of hyperbola.
Now Use these three pints to get the area of triangle.

Thanks.
neena
111 Points
5 years ago
the area of the triangle formed by the the asymptote of a hyperbola and any tangent to the hyperbola is constant and is equal to the product of (semi major axis)*(semi minior axis) for derivation here is a shortcut method.instead of taking any other tangent take the tangent at one vertex and calculate intersection points and thus find the area of the triiangle that comes out to be(a)*(b). if we take other tangent then it will become tough and time waste...

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