If the distance of a variable point \(P\) from a fixed point \((3,-4)\) is \(\dfrac23\) times the distance of \(P\) from the fixed line \(x-y+2=0\), then the locus of \(P\) is
\[
ax^2+4by+by^2-62x+80y+c=0,
\]
then \(2c=\)
Show Hint
A conic can be defined as the locus of a point whose distance from a fixed point (focus) bears a constant ratio to its perpendicular distance from a fixed line (directrix).
Use
\[
\boxed{
\text{Distance from }ax+by+c=0
=
\frac{|ax+by+c|}{\sqrt{a^2+b^2}}.
}
\]