Question

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

Answer 1

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 ^_^