The locus of a point which is at a distance of 2 units from the line 2 x-3 y+4=0 and at a distance of 13 units from a point (5,0) is

Step-by-step solution

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