Example 7. For what values of k does the equation12 x2 -10 x y +2 y2 +

1.	Example 7. For what values of k does the equation12 x2 -10 x y +2 y2 +11x-5 y + k = 0 represents two straight lines?Also find angle between them.
Answer» Step-by-step explanation: Given 2x2−10xy+12y2+5x+λy−3=0 is PAIR of STRAIGHT line So abc+2fgh−af2−bg2−ch2=0 2×12×(−3)+22λ×25×(−5)−2(2λ)2−(12)(25)2−(−3)(−5)2=0 144+25λ+λ2=0 λ=2−25±625−576 λ=2−25±49 λ=2−25±7 λ=−9,−16 But ∣λ∣<16 λ>−16 Hence λ=−9 hope this helps ^_^

Example 7. For what values of k does the equation12 x2 -10 x y +2 y2 +11x-5 y + k = 0 represents two straight lines?Also find angle between them.

Answer»

Step-by-step explanation:

Given

2x2−10xy+12y2+5x+λy−3=0 is PAIR of STRAIGHT line

So abc+2fgh−af2−bg2−ch2=0

2×12×(−3)+22λ×25×(−5)−2(2λ)2−(12)(25)2−(−3)(−5)2=0

144+25λ+λ2=0

λ=2−25±625−576

λ=2−25±49

λ=2−25±7

λ=−9,−16

But ∣λ∣<16

λ>−16

Hence λ=−9

hope this helps ^_^

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Example 7. For what values of k does the equation12 x2 -10 x y +2 y2 +11x-5 y + k = 0 represents two straight lines?Also find angle between them.​

hope this helps ^_^

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Example 7. For what values of k does the equation12 x2 -10 x y +2 y2 +11x-5 y + k = 0 represents two straight lines?Also find angle between them.