Question

If $S=0$ be the equation of the hyperbola $x^2+4xy+3y^2-4x+2y+1=0$, then the value of $k$ for which $S+k=0$ represents its asymptotes is :

• A. $20$
• B. $-16$
• C. $-22$
• D. $18$

Answer 1

The correct option is C $-22$

$S+k=x^2+4xy+3y^2-4x+2y+1+k=0$
For equation $S+k=0$ to represent a pair of lines,
$△=0$
$\left|\begin{array}{ccc}1& 2& -2\\ 2& 3& 1\\ -2& 1& 1+k\end{array}\right|=0$
$\Rightarrow 3(1+k)-1-2(2+2k+2)-2(2+6)=0$
$\Rightarrow k=-22$