The bisectro of the acute angle between the straight lines 3x -4y-3=0 and 12x + 5y +6 =0 passes through which one of the following points?

Options

A. (5,3)
B. (-3,6)
C. (2,7)
D. (-1,4)

Answer

c

Explanation

The equation of given straight lines are
3x-4y-3=0
and 12x+5y+6=0
Re writing equaiton so that costant term in both have same sign we wrtie second equaion so that its constant term is negative then equation of bisectro of the acite angle between the given straight lines is
`(3x-4y-3)/sqrt(3^(2)+4^(32))=(12x+5y+6)/sqrt(12^(2)+5^(2))`
`rarr (3x-4y-3)/(5)=-(12x-5y-6)/(13)`
`rarr 39x-52y-39=-60x-25y-30`
`rarr -60 x-25y-30 -39x+52y+39=0`
`rarr -99x+27y+9=0`
`rarr -11 x+3y+1=0`
Putting x=2 and y =7
this equation is satisfied by (2,7)
Thus the bisectro of acute angle between the given straight lines passes through (2,7)