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If one of the lines $a x^2+2 h x y+b y^2=0$ bisects the angle between the positive coordinate axes, then
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Verified Answer
The correct answer is:
$(a+b)^2=4 h^2$
Equation of angle bisector of line positive coordinate axes is $y=x$
Putting the value of $y=x$ in
$$
\begin{array}{rlrl}
a x^2+2 h x y+b y^2 & =0, \text { we get } \\
a x^2+2 h x^2+b x^2 & =0 \\
\Rightarrow & a+2 h+b & =0 \\
\Rightarrow & a+b & =-2 h \\
\Rightarrow & (a+b)^2 & =4 h^2
\end{array}
$$
Putting the value of $y=x$ in
$$
\begin{array}{rlrl}
a x^2+2 h x y+b y^2 & =0, \text { we get } \\
a x^2+2 h x^2+b x^2 & =0 \\
\Rightarrow & a+2 h+b & =0 \\
\Rightarrow & a+b & =-2 h \\
\Rightarrow & (a+b)^2 & =4 h^2
\end{array}
$$
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