यदि समीकरण निकाय a_(1) x + b_(1) y +c_(1) = 0 तथा a_(2) x + b_(2) y + c_(2) = 0 के लिए (a_(1))/(...

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 .

Consider the system of equations a_(1) x + b_(1) y + c_(1) z = 0 a_(2) x + b_(2) y + c_(2) z = 0 a_(3) x + b_(3) y + c_(3) z = 0 If |(a_(1),b_(1),c_(1)),(a_(2),b_(2),c_(2)),(a_(3),b_(3),c_(3))| =0 , then the system has

For two linear equations a_(1)x + b_(1)y + c_(1)= 0 and a_(2) x+ b_(2)y+ c_(2)= 0 , then condition (a_(1))/(a_(2)) = (b_(1))/(b_(2))= (c_(1))/(c_(2)) is for

If two equation a_(1) x^(2) + b_(1) x + c_(1) = 0 and, a_(2) x^(2) + b_(2) x + c_(2) = 0 have a common root, then the value of (a_(1) b_(2) - a_(2) b_(1)) (b_(1) c_(2) - b_(2) c_(1)) , is

If |(1 +ax,1 +bx,1 + bx),(1 +a_(1) x,1 +b_(1) x,1 + c_(1) x),(1 + a_(2) x,1 + b_(2) x,1 + c_(2) x)| = A_(0) + A_(1) x + A_(2) x^(2) + A_(3) x^(3) , then A_(1) is equal to

The lines a_(1)x + b_(1)y + c_(1) = 0 and a_(2)x + b_(2)y + c_(2) = 0 are perpendicular to each other , then "_______" .

Show that the equation of the straight line through (alpha,beta) and through the point of intersection of the lines a_(1)x+b_(1)y+c_(1)=0 and a_(2)x+b_(2)y+c_(2)=0 is (a_(1)x+b_(1)y+c_(1))/(a_(1)alpha+b_(1)beta+c_(1))=(a_(2)x+b_(2)y+c_(2))/(a_(2)alpha+b_(2)beta+c_(2))