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# If $3x+2y=0$ and $5x-12y=0$ are the equation of the pour of conjugates diameters, then value of eccentricity e is

$\begin{array}{1 1}(A)\;\frac{3}{8} \\(B)\;\frac{1}{2} \sqrt {\frac{3}{2}}\\(C)\;\frac{1}{\sqrt 6} \\(D)\;none\; of\; these \end{array}$

Since, product of the slopes of the pour of conjugate diameter is $\large\frac{-b^2}{a^2}$
$\therefore \large\frac{-b^2}{a^2} =\frac{-3}{2}.\frac{5}{12}$
$1-e^2=\large\frac{5}{8}$
=> $e^2=\large\frac{3}{8}$
$e= \large\frac{1}{2} \sqrt{\frac{3}{2}}$
Hence B is the correct answer.