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)

$11$

Let the other line equation be $ax+by+c=0$,

$\Rightarrow (ax+by+c)(5x+y-1)=0$ is the combined equation,

$\Rightarrow 5a{x}^2+axy-ax+5bxy+b{y}^2-by+5cx+cy-c=0$

$\Rightarrow 5a{x}^2+xy(a+5b)-x(a-5c)-y(b-c)+b{y}^2-c=0$

Given equation is

$\Rightarrow 5a{x}^2+xy-kx-2y+2=0$

comparing this with the original equation gives,

$b=0,a\Rightarrow a+5b=1\Rightarrow a=1,c=-2$,

$\therefore k=a-5c=11$