The bisector of the acute angle formed between the lines 4x - 3y + 7 = 0 and 3x - 4y + 14 = 0 has the equation

Options

A. x + y + 3 = 0
B. x - y - 3 = 0
C. x - y + 3 =0
D. 3x - y - 7 = 0

Answer

C

Explanation

The equations of given straight lines , by making constant terms positive , are
4x - 3y + 7 = 0 and 3x - 4y + 14 = 0
`because 4 xx 3 + (-3) (-4) = 24 gt 0 ` i.e, `a_(1) a_(2) + b_(1)b_(2) gt 0 `
So , the bisector of the acute angle is given by
`(4x - 3y + 7)/(sqrt(4^(2) + (-3)^(2))) = -(3x - 4y + 14)/(sqrt(3^(2) (-4)^(2))) implies x - y + 3 = 0 `