Q97 / 160 · TS EAMCET 2007 · Mathematics

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

  • A
    $2$
  • B
    $4$
  • Correct answer
    C
    $6$
  • D
    $8$

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 $\begin{aligned} & k-3-3=0 \\ & \Rightarrow \quad k=6 \\ & \end{aligned}$

Hence, the correct answer is option: 'C'.

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