A question reads, "Find equation of the line which is equidistant from parallel lines $9x + 6y – 7 = 0$ and $3x + 2y + 6 = 0$."
I solved it by doing the following:-
Finding the distance between the two given lines, halved it to find the distance between the required line which is $9x + 6y + C = 0$ and the line $3x + 2y + 6 =0$.
Took a point $(-2,0)$ lying on the line $3x + 2y + 6 = 0$.
Used the formula for perpendicular distance between a point and a line, but due to modulus, I get two solutions for $C$ (and for the equation).
The two solutions for $C$ are $11/2$ (which is correct) and the other garbage value $61/2$ which is obviously wrong as it would lie above both the given equations as its $y$-intercept is larger than both the equations.
My question is - Why does this garbage value arrive?