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

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

Grade:10

2 Answers

Chetan Mandayam Nayakar
312 Points
10 years ago

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

Chinmay Gore
29 Points
10 years ago

if lines are coincident then h^2 = ab.

so, 12^2 = 9a

so a= 16

 

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