If the slope of one of the lines represented by a x^2-6 x y+y^2=0 is the square of the other, then the value of a is

Step-by-step solution

Given pair of lines, a x^2-6 x y+y^2=0 Let the slope of one line be m , then slope of another line will be m^2 . We know that On cubing Eq. (i) both sides, we get aligned & (m+m^2 )^3=(6)^3 & m^3+m^6+3 m^3 (m+m^2 )=216 & m^3+m^6+18 m^3=216 [ m^3=a ] aligned aligned & a+a^2+18 a=216 & a^2+19 a-216=0 & a^2+27 a-8 a-216=0 & a(a+27)-8(a+27)=0 & (a+27)(a-8)=0 & a=-27,8 aligned