X+2y=3 and 2x+4y=k are represents coincide lines, then value of k is
a)3 b)6 c)-3 d)-6
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The coincident lines are given as,
3x+4y+2=0
And
9x+12y+k=0
Comparing the equations with the general equations
a
1
x+b
1
y+c
1
=0
a
2
x+b
2
y+c
2
=0
Then,
a
1
=3,b
1
=4,c
1
=2,a
2
=9,b
2
=12,c
2
=k
Since, the lines are coincident, then,
a
2
a
1
=
b
2
b
1
=
c
2
c
1
9
3
=
12
4
=
k
2
3
1
=
3
1
=
k
2
3
1
=
k
2
k=6
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