Find the condition for two lines `a_(1)x+b_(1)y+c_(1)=0` and `a_(2)x+b_(2)y+c_(2)=0` to be
`(i)` parallel
`(ii)` perpendicular

If the lines x=a_(1)y + b_(1), z=c_(1)y +d_(1) and x=a_(2)y +b_(2), z=c_(2)y + d_(2) are perpendicular, then

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 .

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 "_______" .

8.If the lines a_(1)x+b_(1)y+c_(1)=0 and a_(2)x+b_(2)y+c_(2)=0 cuts the coordinate axes in concyclic points then

Find the condition for the two concentric ellipses a_(1)x^(2)+b_(1)y^(2)=1 and a_(2)x^(2)+b_(2)y^(2)=1 to intersect orthogonally.

Find the common factors of the expressions a_(1)x^(2)+b_(1)x+c_(1)anda_(2)x^(2)+b_(2)x+c_(1) where c_(1)ne0 .

Show that the lines a_(1)x+b_(1)y+c_(1)=0 and a_(2)x+b_(2)y+c_(2)=0,"where" b_(1),b_(2) ne 0 "are (i) parallel, if"(a_(1))/(b_(1))=(a_(2))/(b_(2))" (ii) perpendicular, if "a_(1)a_(2)+b_(1)b_(2)=0