If a point $(x,y)$ moves on a curve and satisfies the equation $\small\begin{vmatrix}a&b&ax+by\\b&c&bx+cy\\ax+by&bx+ay&0\end{vmatrix}=0$ then

Question

$\begin{array}{1 1}(a)\;a,b,c\;form\;an\;AP\\(b)\;a,b,c\;form\;an\;HP\\(c)\;The\;point(x,y)\;lies \;on\;a\;curve\\(d)\;None\;of\;the\;above\end{array}$