The value of k,if (1,2) and (k,-1) are conjug | vedclass

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(C) The given equation of the ellipse is $2x^2 + 3y^2 = 6$,which can be written as $\frac{x^2}{3} + \frac{y^2}{2} = 1$.Two points $(x_1, y_1)$ and $(x

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$6$

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(C) The given equation of the ellipse is $2x^2 + 3y^2 = 6$,which can be written as $\frac{x^2}{3} + \frac{y^2}{2} = 1$.Two points $(x_1, y_1)$ and $(x_2, y_2)$ are conjugate with respect to the ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ if $\frac{x_1 x_2}{a^2} + \frac{y_1 y_2}{b^2} = 1$.Here,$(x_1, y_1) = (1, 2)$,$(x_2, y_2) = (k, -1)$,$a^2 = 3$,and $b^2 = 2$.Substituting these values into the condition:$\frac{(1)(k)}{3} + \frac{(2)(-1)}{2} = 1$$\frac{k}{3} - 1 = 1$$\frac{k}{3} = 2$$k = 6$.

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

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