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Question

Area of the triangle formed by any tangent to the hyperbola $$\dfrac{{{x^2}}}{{{a^2}}} - \dfrac{{{y^2}}}{{{b^2}}} = 1$$ with its asymptotes is


A
ab
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B
abc
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C
4ab
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D
a2b2
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Solution

The correct option is A $$ab$$
suppose the tangent is at $$(a,o)$$ parallel to y-axis then 
then, $$A(0,0) \,B(a,b) \,C(a,-b) $$
$$BC=2b$$
height $$= a$$
Area $$=\dfrac{1}{2} base\times height = \dfrac{1}{2}\times 2b\times a=ab $$
A is correct.

1072966_1159558_ans_045c07e13e9b4daf92543d5584933335.png

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