Question

If the lines passing through the points $(2,3),(K^2,6)$ and $(6,4),(K,6)$ are parallel, then the total number of possible real values of $K$ is

Answer 1

$m_1=$ Slope of line passing through $(2,3),(K^2,6)$
$=\frac{3}{K^2-2}$
$m_2=$ Slope of line passing through $(6,4),(K,6)$
$=\frac{2}{K-6}$
As lines are parallel. So
$m_1=m_2\Rightarrow \frac{3}{K^2-2}=\frac{2}{K-6}$
$\Rightarrow 3K-18=2K^2-4$
$\Rightarrow 2K^2-3K+14=0$
As $D<0$, so no real value of $K$ is possible.