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From any point on the hyperbola \mathrm{\frac{x^2}{a^2}-\frac{y^2}{b^2}=1} tangents are drawn to the hyperbola  \mathrm{\frac{x^2}{a^2}-\frac{y^2}{b^2}=2}.

The area cut off by the chord of contact on the asymptotes is equal to

 

Option: 1

\mathrm{\frac{ab}{2}}


Option: 2

\mathrm{ab}


Option: 3

\mathrm{2ab}


Option: 4

\mathrm{4ab}


Answers (1)

best_answer

Let \mathrm{\left(\begin{array}{ll} x_1 & y_1 \end{array}\right)} be a point on \mathrm{\frac{x^2}{a^2}-\frac{y^2}{b^2}=1} ,chord to \mathrm{\frac{x^2}{a^2}-\frac{y^2}{b^2}=2} is 

\mathrm{\frac{x x_1}{a^2}-\frac{y y_1}{b^2}-2=0} Asymptote  \mathrm{\frac{x}{a}-\frac{y}{b}=0, \frac{x}{a}+\frac{y}{b}=0}

Area formed by the lines = 4ab

 

Posted by

Irshad Anwar

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