I'm trying to solve this problem from a Precalculus textbook : " find the locus of points $P(x,y)$ such that the distance from $P$ to the $Y$ axis is $5$" . ( Source : Schaum's Outline Of Precalculus).
Note : I know the answer to be found s $ x= + 5$ and $ x= -5$.
The point to straight line distance formula requires to use the $Ax+By+C=0$ form of the equation of this straight line.
I know that the " ordinary" form of the equation of the $Y$ axis : $x=0$.
I've tried to " solve " the general equation " $Ax+By+C=0$ " for $x$ and then set $x=0$.
I found $y= - \frac {C} {AB}$.
Should I substitute this value for $y$ in the point to line distance formula?
I may seem stupid, but I'm stuck.
for $y$-axis, we have $B=C=0$. Also, we can't divide by zero.
The distance formula is
$$\frac{|Ax+By+C|}{\sqrt{A^2+B^2}}=5$$
$$\frac{|Ax|}{|A|}=5$$
$$|x|=5$$