Question

If the equation $12x^{2} - 10xy + 2y^{2} + 11x - 5y + K = 0$represent two straight lines, then the value of K is

• A. 1
• B. 2
• C. 0
• D. 3

Answer 1

Answer: (B)

2

Answer 2

Condition for pair of lines,

$abc + 2fgh - af^{2} - bg^{2} - ch^{2} = 0$, Here $a = 12,h = - 5,b = 2,g = 11/2,f = - 5/2,c = K$

Then, $12 \times 2 \times K + 2 \times \frac{- 5}{2} \times \frac{11}{2} - 12 \times \left( \frac{- 5}{2} \right)^{2} - 2 \times \left( \frac{11}{2} \right)^{2} - K( - 5)^{2} = 0$ On solving, we get K= 2