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P1, P2 are points on either of the two l...

`P_1, P_2` are points on either of the two line `y-sqrt(3)|x|=2` at a distance of `5` units from their point intersection. Find the coordinatesof the foot of perpendiculars drawn from `P_1, P_2` on the bisector of the angle between the given lines.

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Given equation of lines are `y-sqrt3x=2" "[because xge0]`
and `y+sqrt3x=2 " "[because xle0]`
`becausey=sqrt3x+2" "......(i)`
and `y=-sqrt3x+2" ".....(ii)`
`rArrsqrt3x+2=-sqrt3x+2`
`rArr2sqrt3x=0rArrx=0`
On putting x=0in Eq. (i), we get

So, the point of intersection of line (i) and (ii) is (0,2).
Here, OC=2
In `DeltaDEC, (CD)/(CE)=cos 30^@`
`thereforeCD=5cos 30^@=5.sqrt3/(2)`
`rArr OD=OC+CD=2+5sqrt3/(2)`
So, the coordinate of the foot of perpendicular are `(0,2+(5sqrt3)/(2))`
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