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The value of $' k'$ if $(1, 2), (k, - 1)$ are conjugate points with respect to the ellipse $2 x^{2} + 3 y^{2} = 6$ is

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answer is C.

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Detailed Solution

$\frac{x^{2}}{3} + \frac{y^{2}}{2} = 1$

Given conjugate points are:

$(1, 2), (k, - 1)$

$(x_{1}, y_{1}), (x_{2}, y_{2})$

$S_{12} = 0 \Rightarrow \frac{x_{1} x_{2}}{a^{2}} + \frac{y_{1} y_{2}}{b^{2}} = 1$

$\frac{k}{3} - \frac{2}{2} = 1$

$k = 6$

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