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JEE Main & Advanced Mathematics Conic Sections Question Bank Ellipse

  • question_answer
    If \[y=mx+c\] is tangent on the ellipse \[\frac{{{x}^{2}}}{9}+\frac{{{y}^{2}}}{4}=1\], then the value of c is

    A)            0     

    B)            \[3/m\]

    C)            \[\pm \sqrt{9{{m}^{2}}+4}\]    

    D)            \[\pm 3\sqrt{1+{{m}^{2}}}\]

    Correct Answer: C

    Solution :

               Here, \[a=3,\,\,b=2\]. \ By formula, \[{{c}^{2}}={{b}^{2}}+{{a}^{2}}{{m}^{2}}\]                    \ \[{{c}^{2}}=4+9{{m}^{2}}\];  \ \[c=\pm \sqrt{9{{m}^{2}}+4}\].


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