See Fig. The line 4x + 2y = 9 has positive interception coordinates while the line 2x + y + 6 = 0 has negative interception on the axes. Hence, origin O lies in between the axes. Suppose OM and ON, respectively, are drawn perpendicular to the given two lines. Observe O, M and N are collinear (see Fig). Now,

OM = 9/2*√5 and ON = 6/**√5*

If any line through O meets the parallel lines in P and Q, then by pure geometry, we have

OP : OQ = OH : ON = 9/2*√5 : 6/**√5 = 3 : 4*