Q. The value of $k$, if (1, 2), $(k,\ - 1)$ are conjugate points with respect to the ellipse $2x^{2} + 3y^{2} = 6,$ is
A) $2$
B) $4$
C) $6$
D) $8$
Explanation
(c)
Given , $\frac{x^{2}}{3} + \frac{y^{2}}{2} = 1\$
Polar of $P(1,2)$ with respect to ellipse is $S_{1} = 0$
$\Rightarrow \ x + 3y - 3 = 0$
Since, (1,2) and $(k, - 1)$ are conjugates, therefore one passes through the polar of the other.
$k - 3 - 3 = 0$
$\Rightarrow \ k = 6$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.