The number of integral values of $k$ for which $x^2+y^2+\mathrm{k} x+(1-\mathrm{k}) y+5=0$ represents a circle whose radius cannot exceeds 5 , are

The equation of the circle passing through the point $(1,1)$ and having two diameters along the pair of lines $x^2-y^2-2 x+4 y-3=0$ is

If the tangent at $(1,7)$ to the curve $x^2=y-6$ touches the circle $x^2+y^2+16 x+12 y+\mathrm{C}=0$, then $\mathrm{C}=$