Manipal Entrance Test 2016 Math Paper

Equation of line perpendicular to 2x+y+6=0 and passes through origin is x−2y=0
Now, the point of intersection of 2x+y+6=0 and x−2y=0 is (−

12

5

,−

6

5

)
Similarly, the point of intersection of x−2y=0 and 4x+2y−9=0 is (

9

5

,

9

10

).
Let the origin divide the line x−2y=0 in the ratio λ:1
∴x=

9 5 λ− 12 5

λ+1

=0
⇒

9

5

λ=

12

5

⇒λ=

12

9

=

4

3