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A straight line through the origin O meets the parallel lines 4x + 2y = 9 and 2x + y + 6 = 0 at points P and Q, respectively. Then the point O divides the segment PQ in the ratio

(A)  1:2

(B)  3:4

(C)  2:1

(D)  4 : 3

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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

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