Find the value of $4 k$ , if the equation
$3 y^{2} + 9 x y + k x^{2} = 0$ represents a coincident lines.

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Solution

$B y c o m p a r i n g w i t h a x^{2} + 2 h x y + b y^{2} = 0 a = 3, h = (\frac{9}{2}) a n d b = K f o r c o i n c i d e n t l i n e s h^{2} = a b {((\frac{9}{2}))}^{2} = 3 \times K ∴ K = (\frac{81}{4 \times 3}) = (\frac{27}{4})$
$∴ 4 K = 27$ .

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