If the equation of the line joining the points \(A(x_1,y_1)\) and \(B(x_2,y_2)\) is
\[
ax+by=c
\]
and the distance between \(A\) and \(B\) is \(\sqrt{a^2+b^2}\), then \(c^2=\)
Show Hint
The equation of the line through
\[
(x_1,y_1)\ \text{and}\ (x_2,y_2)
\]
can be written as
\[
\boxed{
(y_2-y_1)x-(x_2-x_1)y=x_1y_2-x_2y_1.
}
\]
The constant term directly gives the required value of \(c\).