11th Class Mathematics Conic Sections Question Bank Critical Thinking

  • question_answer If the angle between the lines joining the end points of minor axis of an ellipse with its foci is \[{{x}^{2}}-{{y}^{2}}=25\], then the eccentricity of the ellipse is [IIT Screening 1997; Pb. CET 2001; DCE 2002]

    A)            1/2 

    B)            \[1/\sqrt{2}\]

    C)            \[\sqrt{3}/2\]                            

    D)            \[1/2\sqrt{2}\]

    Correct Answer: B

    Solution :

               Since \[\angle \,FBF'=\frac{\pi }{2}\] (Given) \[\therefore \]\[\angle \,FBC=\,\angle \,F'BC=\pi /4\]                      \[CB=CF\Rightarrow \,\,b=ae\] Þ \[{{b}^{2}}={{a}^{2}}{{e}^{2}}\]                   Þ \[{{a}^{2}}(1-{{e}^{2}})={{a}^{2}}{{e}^{2}}\]            Þ \[1-{{e}^{2}}={{e}^{2}}\] Þ \[2{{e}^{2}}=1\] Þ \[e=1/\sqrt{2}\].

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