3.2.16 Lines on a plane

Condition: Let the sides \( A B \) and \( A D \) of the rhombus \( A B C D \) be located on the lines \( a_{1} x+b_{1} y+c_{1}=0 \) and \( a_{2} x+b_{2} y+c_{2}=0 \) respectively, and \( P\left(x_{p} ; y_{p}\right) \) - the point of intersection of its diagonals. Find a) the coordinates of the vertices of the rhombus; b) equations of the sides \( B C, D C \) and diagonals of a rhombus; c) area of ​​a rhombus. Make a drawing. Input data: \begin{tabular}{|c|c|c|c|c|c|c|c|} \hline\( x_{p} \) & \( y_{p} \) & \( a_{1} \) & \( b_{1} \) & \( c_{1} \) & \( a_{2} \) & \( b_{2} \) & \( c_{2} \) \\ \hline 13 & 12 & 3 & -4 & 2 & 4 & -3 & -9 \\ \hline \end{tabular}