If the slope of one of the lines represented by a x^2+(2 a+1) x y+2 y^2=0 is reciprocal of the slope of the other, then the sum of squares of slopes is

Step-by-step solution

Given equation of pair of lines is aligned & a x^2+(2 a +1) x y+2 y^2=0 & ~A = a , H = 2 a +1 2 , ~B =2 aligned Given condition, array ll & m ₁= 1 ~m ₂ & m ₁ m ₂=1 & Product of slopes = A B = a 2 & m ₁ m ₂=1= a 2 & a =2 & Also, sum of slopes = -2 H B =- ( 2 a +1 2 )= -5 2 & Using ( m ₁+ m ₂ )^2= m ₁^2+ m ₂^2+2 ~m ₁ ~m ₂ & ( -5 2 )^2= m ₁^2+ m ₂^2+2 1 & m ₁^2+ m ₂^2= 25 4 -2 & m ₁^2+ m ₂^2= 17 4 array