The equation of the pair of lines passing through the origin whose sum and product of slopes are respectively the arithmetic mean geometric mean of 4 and 9 is

Question

\[(a)\;12x^2-13xy+2y^2=0\quad (b)\;12x^2+13xy+2y^2=0 \quad (c)\;12x^2-15xy+2y^2=0 \quad (d)\;12x^2+15xy-2y^2=0 \]