Let (1,2) be the focus and x+y+1=0 be the directrix of a hyperbola H . If 3 is the eccentricity of H , then its equation is

Step-by-step solution

Given equation of directrix is x+y+1=0 and Focus is (1,2)=5 Let P(x, y) be any point on hyperbola H Let PM be the length of the perpendicular from P to the directrix. then P S P M = 3 P S^2=3 P M^2 aligned & (x-1)^2+(y-2)^2=3 | x+y+1 2 |^2 & aligned 2 (x^2+1-2 x+y^2+4-4 y )=3 (x^2+y^2+1 . & +2 x y & +2 y+2 x) 2 x^2+2-4 x+2 y^2+8-8 y=3 x^2+3 y^2+3 & +6 x y +6 y+6 x x^2+y^2+6 x y+10 x+14 y-7=0 & aligned aligned