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If $a x^2-34 x y-5 y^2+2 x+26 y-5=0$ represents a pair of straight lines, then the value of $a$ is
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Verified Answer
The correct answer is:
$7$
$$
a x^2-34 x y-5 y^2+2 x+26 y-5=0
$$
Here, $\Delta=\left|\begin{array}{ccc}a & -17 & 1 \\ -17 & -5 & 13 \\ 1 & 13 & -5\end{array}\right|=0$
$$
\begin{aligned}
& {\left[\left|\begin{array}{lll}
a & h & g \\
h & b & f \\
g & f & c
\end{array}\right|=0\right]} \\
& \Rightarrow a(-144)+17(72)-216=0 \\
& \Rightarrow \quad a=7 \\
&
\end{aligned}
$$
a x^2-34 x y-5 y^2+2 x+26 y-5=0
$$
Here, $\Delta=\left|\begin{array}{ccc}a & -17 & 1 \\ -17 & -5 & 13 \\ 1 & 13 & -5\end{array}\right|=0$
$$
\begin{aligned}
& {\left[\left|\begin{array}{lll}
a & h & g \\
h & b & f \\
g & f & c
\end{array}\right|=0\right]} \\
& \Rightarrow a(-144)+17(72)-216=0 \\
& \Rightarrow \quad a=7 \\
&
\end{aligned}
$$
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