A point $P(a,b)$ is equidistant from the y-axis and from the point $(4,0)$. Find a relationship between $a$ and $b$.
I know that the distance of $(a,b)$ from the point $(4,0)$ is $\sqrt {(a-4)^2+b^2}$
I can make an equation using the equations of the lengths of $(a,b)$ from the y-axis and the point $(4,0)$ and make them equal each other. But I don't see how I can find the distance of $(a,b)$ from the y-axis.
A straight, horizontal line being formed from the point $P(a,b)$ and the y-axis will have length $\sqrt {(a-0)^2+(b-b)^2}$, as the point on the y-axis will have coordinates $(0,b)$.
$\sqrt {(a-0)^2+(b-b)^2} \Rightarrow \sqrt {a^2}$
If the point $P(a,b)$ is equidistant from the y-axis and the point $(4,0)$, we can write:
$\sqrt {a^2}=\sqrt {(a-4)^2+b^2} \Rightarrow a^2=(a-4)^2+b^2 \Rightarrow a^2=a^2-8a+16+b^2 \Rightarrow b^2=8a-16$