The length of the intercept on the line $$4 x-3 y-10=0$$ by the circle $$x^2+y^2-2 x+4 y-20=0$$ is

The pole of the line $$\frac{x}{a}+\frac{y}{b}=1$$ with respect to the circle $$x^2+y^2=c^2$$ is

If the tangent at the point $$P$$ on the circle $$x^2+y^2+6 x+6 y=2$$ meets the straight line $$5 x-2 y+6=0$$ at a point $$Q$$ on the $$Y$$-axis, then the length of $$P Q$$ is

Suppose a parabola with focus at $$(0,0)$$ has $$x-y+1=0$$ as its tangent at the vertex. Then, the equation of its directrix is