Thank you for reporting, we will resolve it shortly
Q.
The real value of a for which the value of $m$ satisfying the equation $\left(a^{2}-1\right) m^{2}-(2 a-3) m+a=0$ gives the slope of a line parallel to the $y$-axis is
Straight Lines
Solution:
A line parallel to the $y$-axis has slope $\infty$.
Therefore, $\left( a ^{2}-1\right) m ^{2}-(2 a -3) m + a =0$ must have one infinite root.
So, $a^{2}-1=0$ since both roots cannot be $\infty$ for then $a^{2}-1$ $=0$ and $2 a -3 \neq 0$ are to hold for the same $a$.