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# If the pair of lines $ax^2+2hxy +by^2+2gx+ 2fy+c=0$ intersect on the y-axis then

$\begin{array}{1 1}(A)\;2fgh=bg^2+ch^2\\(B)\;bg^2 \neq ch^2 \\(C)\;abc=2fgh \\(D)\;none\; of\; these \end{array}$

Put $x=0$ in the given equation
=>$by^2+2fy+c=0$
For unique point of intersection.
$f^2-bc=0$
=>$af^2-abc=0$
Since $abc+2fgh-af^2-bg^2-ch^2=0$
=> $2fgh-bg^2-ch^2=0$
Hence A is the correct answer.