If the length of the chord of the line
\[
x+y-1=0
\]
of the circle
\[
x^2+y^2-6x+2fy-2=0\qquad(f>0)
\]
is
\[
\frac{6\sqrt7}{\sqrt2},
\]
then the length of the intercept made by this circle on the \(Y\)-axis is
Show Hint
The length of a chord at perpendicular distance \(d\) from the centre is
\[
\boxed{2\sqrt{r^2-d^2}}.
\]
To find the intercept on an axis, substitute the corresponding coordinate (\(x=0\) or \(y=0\)) in the circle equation.