The circle $x^2+y^2+4x-7y+12=0$ cuts an intercept on y-axis of length

The circle $x^2+y^2+2gx+2fy+c=0$ cuts an intercept of length $2\sqrt{f^2-c}$ y-axis

For the circle $x^2+y^2+4x-7y+12=0$,we have

$\begin{array}{l}g=2,f=-7/2\text{ and }c=12\\ \therefore y\text{-intercept }=2\sqrt{f^2-c}=2\sqrt{\frac{49}{4}-12}=1.\end{array}$