HyperbolaHardBloom L3
Question
The tangent to the hyperbola, $x^{2} - 3y^{2} = 3$ at the point $(\sqrt{3},0)$ when associated with two asymptotes constitutes:
Options
A.scalene triangle
B.an equilateral triangle
C.a triangle whose area is $\sqrt{3}$ sq. units
D.a right isosceles triangle
Solution
Sol. (b, c)
In $\bigtriangleup AOB$,
$$OA = 2 = OB = AB$$
Area of $\bigtriangleup AOB = \frac{\sqrt{3}}{4}(2)^{2} = \sqrt{3}$
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