Question

If the equation kxy + 5x + 3y + 2 = 0 represents a pair of lines, then k = ____________.

विकल्प

• `15/2`

• 15

• `0, -15/2`

• `1, 15/2`

Answer 1

If the equation kxy + 5x + 3y + 2 = 0 represents a pair of lines, then k = `underline(15/2)`.

Explanation:

Given equation of pairs of lines

kxy + 5x + 3y + 2 = 0

We know that, if ax² + 2hxy + by² + 2gx + 2fy + c = 0 is a pair of straight line, then

abc + 2fgh − af² − bg² − ch² = 0

in equation, kxy + 5x + 3y + 2 = 0

Here, a = 0, b = 0, h = `"k"/2`, g = `5/2`, f = `3/2`, c = 2

∴ `0 + 2(5/2) (3/2) ("k"/2) - 0 - 0 - 2("k"/2)^2` = 0

`(15"k")/4 - "k"^2/2` = 0

`"k"/2 (15/2 - "k")` = 0

k = `15/2` k ≠ 0, if k = 0

Then only one straight line.