MathematicsThe line 3x-3y+17=0 bisects the angle between a pair of lines of which one line is 2x+y+4=0, then the equation to the other line is

The line 3x-3y+17=0 bisects the angle between a pair of lines of which one line is 2x+y+4=0, then the equation to the other line is

  1. A

    3x+6y5=0

  2. B

    3x+6y7=0

  3. C

    7xy+14=0

  4. D

    4xy+3=0

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    Solution:

    Givenlines3x3y+17=0(1)slope=12x+y+4=0(2)slope=2solving  (1)&(2)             x           y         1317331421x1217=y3412=13+6x29=y22=19P(299,229)

    LetRequiredEquationy229=m(x+299)(3)If(1)  is  anglebisectorof(2)&(3)  thenAngleb/w(1)&(3)=Angleb/w(1)&(2)|m11+m|=|1+212||m11+m|=3Ifm11+m=3,Ifm11+m=3m1=3+3m,m1=33m2m=4,4m=2m=2,m=12

    m=12  from(3)y229=12(x+299)2(9y22)=(9x+29)18y44=9x299x+18y15=03x+6y5=0

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