Question

Find ‘k’, if the equation kxy + 10x + 6y + 4 = 0 represents a pair of straight lines.

Answer 1

Given equation is kxy + 10x + 6y + 4 = 0

Comparing with ax² + 2hxy + by² + 2gx + 2fy + c = 0, we get

a = 0, h = k/2 , b = 0, g = 5, f = 3, c = 4

Since the given equation represents a pair of lines.
abc + 2fgh - af² - bg² -ch² = 0

(0)(0)(4)+2(3)(5)(k/2)-(0)(3)^2-(0)(5)^2-4(k/2)^2=0

15k - k² = 0
- k² + 15k = 0
- k(k - 15) = 0
 k = 0 or k = 15
If k = 0, then the equation becomes
10x + 6y + 4 = 0 which does not represents a pair of lines.
 k ≠ 0
Hence, k = 15.