If the three lines `a x+a^2y+1=0,\ b x+b^2y=1=0\ a n d\ c x+c^2y+1=0` are concurrent, show that at least two of three constants `a , b ,\ c` are equal.

If the lines x+a y+a=0,\ b x+y+b=0\ a n d\ c x+c y+1=0 are concurrent, then write the value of 2a b c-a b-b c-c adot

If the lines a x+2y+1=0,b x+3y+1=0a n dc x+4y+1=0 are concurrent, then a ,b ,c are a. A.P. b. G.P. c. H.P. d. none of these

If the lines a x+12 y+1=0,\ b x+13 y+1=0 and c x+14 y+1=0 are concurrent, then a , b , c are in a. H.P. b. G.P. c. A.P. d. none of these

If a ,\ b ,\ c are in A.P. prove that the straight lines a x+2y+1=0,\ b x+3y+1=0\ a n d\ c x+4y+1=0 are concurrent.

If the straight lines x+y-2=0,2x-y+1=0 and a x+b y-c=0 are concurrent, then the family of lines 2a x+3b y+c=0(a , b , c are nonzero) is concurrent at (a) (2,3) (b) (1/2,1/3) (c) (-1/6,-5/9) (d) (2/3,-7/5)

If the lines a x+2y+1=0,b x+3y+1=0a n dc x+4y+1=0 are concurrent, then a ,b ,c are in (a). A.P. (b). G.P. (c). H.P. (d). none of these

If the straight lines x+y-2-0,2x-y+1=0 and a x+b y-c=0 are concurrent, then the family of lines 2a x+3b y+c=0(a , b , c) are nonzero) is concurrent at (a) (2,3) (b) (1/2,1/3) (c) (-1/6,-5/9) (d) (2/3,-7/5)

For what value of lambda are the three lines 2x-5y+3=0,\ 5x-9y+lambda=0\ a n d\ x-2y+1=0 concurrent?

If the lines a x+y+1=0,x+b y+1=0 and x+y+c=0 are concurrent (a!=b!=c!=1) , prove that 1/(1-a)+1/(1-b)+1/(1-c)=1 .

The straight lines x+2y-9=0,3x+5y-5=0 , and a x+b y-1=0 are concurrent, if the straight line 35 x-22 y+1=0 passes through the point (a , b) (b) (b ,a) (-a ,-b) (d) none of these