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JEE Main & Advanced Mathematics Conic Sections Question Bank Ellipse

  • question_answer
    In the ellipse \[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1\], the equation of diameter conjugate to the diameter \[y=\frac{b}{a}x\], is

    A)            \[y=-\frac{b}{a}x\]                    

    B)            \[y=-\frac{a}{b}x\]

    C)            \[x=-\frac{b}{a}y\]                    

    D)            None of these

    Correct Answer: A

    Solution :

               \[y=\frac{-b}{a}x\](Two diameter \[y={{m}_{1}}x\]and \[y={{m}_{2}}x\]will be conjugate diameter, if \[{{m}_{1}}{{m}_{2}}=-\frac{{{b}^{2}}}{{{a}^{2}}}\]).


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