Question

If the lines given by 3x + 2ky = 2 and 2x + 5y + 1 = 0 are parallel, then the value of k is ______.

Options

• `(-5)/4`

• `2/5`

• `15/4`

• `3/2`

Answer 1

If the lines given by 3x + 2ky = 2 and 2x + 5y + 1 = 0 are parallel, then the value of k is `15/4`.

Explanation:

Given equation of lines are

3x + 2ky –2 = 0 and 2x + 5y + 1 = 0

Here a₁ =3 

b₁ = 2k

c₁ = –2

And a₂ = 2

b₂ = 5

c₂ = 1

Since condition for parallel lines is

`a_1/a_2 = b_1/b_2 ≠ c_1/c_2`

∴ `3/2 = (2k)/2`

⇒ k = `15/4`