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JEE Main & Advanced Sample Paper JEE Main Sample Paper-26

  • question_answer
    If the variable line \[y=kx+2h\] is tangent to an ellipse \[2{{x}^{2}}+3{{y}^{2}}=6\], then locus of P(h, k) is a conic C whose eccentricity equals

    A)  \[\frac{\sqrt{5}}{2}\]                            

    B)  \[\frac{\sqrt{7}}{3}\]

    C)  \[\frac{\sqrt{7}}{2}\]                            

    D)  \[\sqrt{\frac{7}{3}}\]

    Correct Answer: A

    Solution :

    By using condition of tangency, we get \[4{{h}^{2}}\,=3{{k}^{2}}+2\] \[\therefore \] Locus of P(h, k) is \[4{{x}^{2}}-3{{y}^{2}}=2\] (which is hyperbola.) Hence, \[{{e}^{2}}=1+\frac{4}{3}\Rightarrow \,e=\sqrt{\frac{7}{3}}\]


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