[" 53.If "(1)/(ab')+(1)/(ba')=0," then lines "(x)/(a)+(y)/(b)=1" and "],[(x)/(b')+(y)/(a')=1" are "quad [" MIP PET "1984]]

Angle between the lines (x)/( a) + (y)/( b) and (x)/(a) - (y)/( b) = 1 is ….....

If ab +bc+ca=0 , show that the lines (x)/(a)+(y)/(b)=(1)/(c),(x)/(b)+(y)/(c)=(1)/(a) and (x)/(c)+(y)/(a)=(1)/(b) are concurrent.

If the slope of the line ((x)/(a)+(y)/(b)-1)+k((x)/(b)+(y)/(a)-1)=0 is -1 then the value of k=?

If (x)/(c)+(y)/(d)=1 be any line passing through the intersection of the lines (x)/(a)+(y)/(b)=1 and (x)/(b)+(y)/(a)=1, then

Show that the tangent of an angle between the lines (x)/(a) + (y)/( b) = 1 and (x)/( a) - (y)/( b) = 1 is (2 ab)/( a^(2) - b^(2) ) .

If (x)/(l)+(y)/(m)=1 is any line passing through the intersection point of the lines (x)/(a)+(y)/(b)=1 and (x)/(b)+(y)/(a)=1 then prove that (1)/(l)+(1)/(m)=(1)/(a)+(1)/(b)

Prove that the following sets of three lines are concurrent: (x)/(a)=(y)/(b)=1,(x)/(b)+(y)/(a)=1 and y=x

Show that the tangent of an angle between the lines (x)/(a)+(y)/(b)=1 and (x)/(a)-(y)/(b)=1 and (2ab)/(a^(2)-b^(2)) .

Show that the tangent of an angle between the lines (x)/(a)+(y)/(b)=1 and (x)/(a)-(y)/(b)=1 and (2ab)/(a^(2)-b^(2)) .

Prove that the diagonals of the parallelogram formed by the four lines : (x)/(a)+(y)/(b)=1 , (x)/(a)+(y)/(b)=-1 , (x)/(a)-(y)/(b)=1 , (x)/(a)-(y)/(b)=-1 are at right angles.