Question

If the equation 3x² + 10xy + 3y² + 16y + k = 0 represents a pair of lines, then the value of k is ______.

पर्याय

• - 21

• 12

• - 12

• 21

Answer 1

If the equation 3x² + 10xy + 3y² + 16y + k = 0 represents a pair of lines, then the value of k is - 12.

Explanation:

Given equation,

3x² + 10xy + 3y² + 16y + k = 0 represents a pair of line

Here, a = 3, b = 3, c = k, h = 5, g = 0, f = 8

For pairs of straight line

abc + 2fgh - af² - bg² - ch² = 0

∴ 9k + 0 - 192 - 0 - 25k = 0

16k = - 192

k = - `192/16` = - 12