Question

The line $5x + y - 1 = 0$ coincides with one of the lines given by $5x^2 + xy - kx - 2y + 2 = 0$ then the value of k is

• A. -11
• B. 31
• C. 11
• D. -31

Answer 1

Answer: (C)

11

Answer 2

Given, $5 x+y-1=0$ coincides with one of the lines given by
$5 x^{2}+x y-k x-2 y+2=0$
On putting the value of $y=-5 x+1$ in the above equation,
we get
$5 x^{2}+x(-5 x+1)-k x-2(-5 x+1)+2=0$
$\Rightarrow 5 x^{2}-5 x^{2}+x-k x+10 x-2+2=0$
$\Rightarrow x-k x+10 x=0$
$\Rightarrow 11 x-k x=0$
$\Rightarrow 11-k=0$
$\Rightarrow k=11$