The locus of a point which is at a distance of 2 units from the...

Let $P(h, k)$ be the point whose locus is to be find. given $\sqrt{(h-5)+(k-0)^2}=\sqrt{13}$ \Rightarrow h²=-k²+10 h-12...(1) also given, $\frac{2 h-3 k+4}{\sqrt{4+9}}=2$ Squaring both sides, we get- \Rightarrow 4 h²+9 k²+16-12 h k-24 k+16 h=52 Putting $h^2$ value in above equation we get \Rightarrow 12 h k-5 k²-56 h+24 k+84=0 for getting locus replacing $h, k$ by $x, y$ respectively \Rightarrow 12 x y-5 y²-56 x+24 y+84=0