Question

If the lines given by 2x+2ky=2 and 2x+5y+1=0 are parallel,then the value of k is ​

Answer 1

Answer:

Condition for the lines to be parallel is

a

2

a

1

=

b

2

b

1



=

c

2

c

1

Here the equations are

3x+2ky=2 and 2x+5y+1=0

So, a

1

=3,b

1

=2k,c

1

=−2 and a

2

=2,b

2

=5,c

2

=1

∴

a

2

a

1

=

2

3

,

b

2

b

1

=

5

2k

and

c

2

c

1

=

1

−2

=−2

∴

5

2k

=

2

3

∴k=

4

15

Answer 2

Answer:

Condition for the lines to be parallel is

a

2

a

1

=

b

2

b

1



=

c

2

c

1

Here the equations are

3x+2ky=2 and 2x+5y+1=0

So, a

1

=3,b

1

=2k,c

1

=−2 and a

2

=2,b

2

=5,c

2

=1

∴

a

2

a

1

=

2

3

,

b

2

b

1

=

5

2k

and

c

2

c

1

=

1

−2

=−2

∴

5

2k

=

2

3

∴k=

4

15