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

Dear Pranavi,

y=kx,(2+k)x=-6,

x=-6/(k+2),y=-6k(k+2),this is Q

now P:(4+2k)x=9

x=9/(4+2k),y=9k/(4+2k)

OP=(9/(4+2k))√(1+k²)

OQ=-(6/(2+k))√(1+k²)

lOP/OQl=l-(9/6)*(k+2)/(2k+4)l=3/4

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CHETAN MANDAYAM NAYAKAR

PO : OQ = 3:4

 2y = -4x + 9

2y = -4x - 12

The y-intercepts of these two lines are +9/2 and -12/2, respectively. The origin divides the segment as

9:12 = 3:4