Find K if the equation represents a pair of lines x^(2)-y^(2)+2x+k=0
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Answer:
Given equation is 3x
2
+10xy+3y
2
+16y+k=0
Comparing it with ax
2
+2hxy+by
2
+2gx+2fy+c=0
We get, a=3,h=5,b=3,g=0,f=8,c=k
The equation represents pair of straight lines.
∴ abc+2fgh−af
2
−bg
2
−ch
2
=0
⇒ 3×3×k+2×8×0×5−3(8)
2
−3(0)
2
−k(5)
2
=0
⇒ 9k+0−192−0−25k=0
⇒ −16k−192=0
⇒ −16k=192
∴ k=−12
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