if ax^2+12xy+9y^2=0 represents two coincident lines then find the value of a

for coincident lines, ax^2 +12xy +9y^2 should be a perfect square. upon completing the square,we get ax^2+12xy+9y^2

=(x√a +3y)², from inspection, it is obvious that ax^2 =4x^2, a=4

if lines are coincident then h^2 = ab.

so, 12^2 = 9a

so a= 16