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
B
abc
C
4ab
D
a2b2

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.Maths

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