Statement - 1 : For the straight lines 3x - 4y + 5 = 0 and 5x + 12 y - 1 = 0 , the equation of the bisector of the angle which contains the origin is 16 x + 2 y + 15 = 0 and it bisects the acute angle between the given lines .
statement - 2 : Let the equations of two lines be `a_(1) x + b_(1) y + c_(1) = 0` and `a_(2) x + b_(2) y + c_(2) = 0` where `c_(1)` and `c_(2)` are positive . Then , the bisector of the angle containing the origin is given by
`(a_(1) x + b_(1) y + c_(1))/(sqrt(a_(2)^(2) + b_(1)^(2))) = (a_(2) x + b_(2)y + c_(2))/(sqrt(a_(2)^(2) + b_(2)^(2)))`
If `a_(1) a_(2) + b_(1) b_(2) gt 0` , then the above bisector bisects the obtuse angle between given lines .

Options

A. Statement -1 is True , Statement - 2 is true , Statement- 2 is a correct explanation for statement - 11
B. Statement-1 is True , Statement-2 is True , Statement -2 is not a correct explanation for Statement - 1 .
C. Statement-1 is True , Statement - 2 is False .
D. Statement - 1 is False , Statement -2 is True .

Answer

D

Explanation

Statement - 2 is true . Using statement -2 , we obtain 16 x + 2y + 15 = 0 as the bisector of the angle containing the origin but it bisects the obtuse angle between the given lines . So , statement - 1 is not true .