If the slope of one of the two lines x^2 a + 2 x y h + y^2 b =0 is twice that of the other, then a b: h^2=

Step-by-step solution

aligned & x^2 a + 2 x y h + y^2 b =0 & 1 b ( y x )^2+ 2 h ( y x )+ 1 a =0 & m₁+m₂= -2 h 1 b = -2 b h and m₁ m₂= 1 a 1 b = b a aligned aligned & from (1) and 2 ( -2 b 3 h )^2= b a & 2 4 b^2 9 h^2 = b a & a b h^2 = 9 8 =9: 8 aligned