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Obtaining Centre and Radius of a Circle from General Equation of a Circle

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Question

Find the value of $k$ , if the equation $k x^{2} - 12 x y + 4 y^{2} = 0$ represents coincident lines.

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Solution

$I f e q^{n} o f l i n e i s a x^{2} + 2 b x y + b y^{2} = 0 c o i n c i d e n t l i n e h^{2} = a b i n o u r c a s e (- 6)^{2} = k \cdot 4 k = (\frac{36}{4}) = 9$

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