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If \mathrm{\alpha+\beta=3 \pi}  then the chord joining the points \mathrm{\text { ' } \alpha \text { ' and } \beta^{\prime}}   for hyperbola \mathrm{\frac{x^2}{a^2}-\frac{y^2}{b^2}=1} passes through 

Option: 1

Focus


Option: 2

centre


Option: 3

one of end points of transverse axis


Option: 4

one of end points of conjugate axis

 


Answers (1)

best_answer

equation of the chord joining \alpha \; and \; \beta is \mathrm{\frac{x}{a} \cos \left(\frac{\alpha-\beta}{2}\right)-\frac{y}{b} \sin \left(\frac{\alpha+\beta}{2}\right)=\cos \left(\frac{\alpha+\beta}{2}\right)}

\mathrm{\text { but } \alpha+\beta=3 \pi \Rightarrow \frac{x}{a} \cos \left(\frac{\alpha-\beta}{2}\right)+\frac{y}{b}=0}

it passes through (0,0)

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Ritika Harsh

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