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
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
$2$
$4$
$6$
$8$
Solution
Given ellipse is $2 x^2+3 y^2=6$ $\Rightarrow \quad \frac{x^2}{3}+\frac{y^2}{2}=1$
Polar of $P(1,2)$ with respect to ellipse is $S_1=0$. $\Rightarrow \quad x+3 y-3=0$
Since, $(1,2)$ and $(k,-1)$ are conjugates, therefore one passes through the polar of the other
$\begin{aligned} & k-3-3=0 \\ & \Rightarrow \quad k=6 \\ & \end{aligned}$