The product of the perpendicular distances from (2,-1) to the pair of lines 2 x^2-5 x y+2 y^2=0 is

Step-by-step solution

aligned & 2 x^2-5 x y+2 y^2=0 & 2 x^2-4 x y-x y+2 y^2=0 2 x(x-2 y)-y(x-2 y)=0 & (2 x-y)(x-2 y)=0 aligned Thus lines are 2 x-y=0 and x-2 y=0 Distance of point (2,-1) from these two lines are respectively | (2)(2)+(-1)(1) 4+1 | and | (1)(2)+(-1)(-2) 1+4 | i.e. 5 5 and 4 5 Hence required answer is 5 5 4 5 =5