Mathematics - Circle Question with Solution | TestHub

A circle $\mathrm{S}=0$ touches a circle $x^2+y^2-4x+6y-23=0$ internally and the circle $x^2+y^2-4x+8y+19=0$ externally. The locus of centre of the circle $\mathrm{S}=0$ is conic whose eccentricity is k then $\left[\frac{1}{k}\right]$ is where [.] denotes G.I.F