Values of |K| so that equation 16x2 + 24xy + ly2 + kx – 12y – 21 = 0 represents a pair of parallel lines is _____

Apply h2=ab and af2=bg2 ⇒144=16l ⇒l=9 and 16(36)=9(k24) ⇒k2=256 ⇒k=16

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Values of |K| so that equation 16x² + 24xy + ly² + kx – 12y – 21 = 0 represents a pair of parallel lines is _____

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answer is 16.

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Detailed Solution

$Apply h^{2} = ab a n d {af}^{2} = {bg}^{2} \Rightarrow 144 = 16 l \Rightarrow l = 9 a n d 16 (36) = 9 (\frac{k^{2}}{4}) \Rightarrow k^{2} = 256 \Rightarrow |k| = 16$

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