Question

A straight line through the origin O meets the parallel lines
4x+2y=9 and 2x+y+6=0 at points Pand 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

Answer 1

• Given,
• A straight line through the origin O meets the parallel lines

       4x+2y=9 and 2x+y+6=0 at points Pand Q respectively.

• One of the ways in which this problem can be solved is,
• let equations be a1x+b1y+c1=0 and a2x+b2y+c2=0

• So, Distance of origin from given line 4x+2y-9=0 is,

     = |-9|/$\sqrt{16+4}$

     =9/20

• Next,

• Distance of origin from given line 2x+y+6=0 is/

      =|6|/$\sqrt{2^{2} +1^{2} }$

      =6/√5

• Therefore, the required ratio is,

     =$\frac{9/\sqrt{20} }{6/\sqrt{5} }$

     =3/4

     ⇒3:4

∴The point o divides the segment PQ in the ratio 3:4

Answer 2

Answer:

Step-by-step explanation: