As, we know that, the general equation of second degree ax2+2hxy+by2+2gx+2fy+c=0 represents a pair of straight lines if and only if ∆=0. Where ∆=|
a
h
g
h
b
f
g
f
c
|=abc+2fgh−af2−bg−ch2 Now, 2x2−xy+ky2+6x+y+4=0 represents a pair of straight lines, if |
2
−‌
1
2
3
−‌
1
2
k
‌
1
2
3
‌
1
2
4
|=0 Here, a= coefficient of x2=2 b‌‌=‌ coefficient of ‌y2=k 2h‌‌=‌ coefficient of ‌xy=−1 ⇒‌‌h‌‌=−‌
1
2
2g‌‌=‌ coefficient of ‌x=6 g‌‌g‌‌=3 2f‌‌=‌ coefficient of ‌y=1 ⇒‌‌f‌‌=1∕2 c‌‌=‌ constant term ‌=4 ⇒2(4k−‌