Find the value of k if the following equations represent a pair of lines : x^2 + 3xy + 2y^2 + x – y + k = 0

Question

Find the value of k if the following equation represent a pair of lines :

x² + 3xy + 2y² + x – y + k = 0

Answer 1

Comparing the given equation with

ax² + 2hxy + by² + 2gx + 2fy + c = 0,

we get, a = 1, h = 3/2, b = 2, g = 1/2, f= 1/2, c = k.

Now, given equation represents a pair of lines.

Taking out 1/2 common from each row , we get,

∴ 2(8k – 1) – 3(6k + 1) + 1(-3 – 4) = 0 

∴ 16k – 2 – 18k – 3 – 7 = 0 

∴ -2k – 12 = 0 

∴ -2k = 12 

∴ k = -6.