If `(a_1x^2 +b_x+c_1)y+(a_2x^2+b_2x+c_1)=0` find condition that x is a rational function of y.

a_1x+b_1y+c_1=0, a_2x+b_2y+c_2=0 Under what condition the above equations represent a unique solution.

a_1x+b_1y+c_1=0, a_2x+b_2y+c_2=0 Under what condition the above equations represent infinitely many solution.

If a_1x^2 + b_1 x + c_1 = 0 and a_2x^2 + b_2 x + c_2 = 0 has a common root, then the common root is

If (a_1)/( a_2) =(b_1)/( b_2) = (C_1) /( c_2) where a_1x +b_1y +c_1=0 and a_2x +b_2y +c_2 =0, then the given pair of linear equation has …………… solutions

If the two lines a_1x + b_1y + c_1 = 0 and a_2x + b_2y + c_2 = 0 cut the co-ordinates axes in concyclic points. Prove that a_1a_2 = b_1b_2

a_1x+b_1y+c_1=0 and a_2x+b_2y+c_2=0 has no solution if _________.

If the lines a_1x+b_1y+c_1=0 and a_2x+b_2y+c_2=0 cut the coordinae axes at concyclic points, then prove that |a_1a_2|=|b_1b_2|

If the lines a_1x+b_1y+c_1=0 and a_2x+b_2y+c_2=0 cut the coordinae axes at concyclic points, then prove that a_1a_2=b_1b_2

If the lines a_1x+b_1y+c_1=0 and a_2x+b_2y+c_2=0 cut the coordinae axes at concyclic points, then prove that |a_1a_2|=|b_1b_2|

If a_1x^3 + b_1x² + c_1x + d_1 = 0 and a_2x^3 + b_2x^2+ c_2x + d_2 = 0 have a pair of repeated common roots, then prove that |[3a_1,2b_1,c_1],[3a_2,2b_2,c_2],[a_2b_1-a_1b_2,c_1a_2-c_2a_1,d_1a_2-d_2a_1]|=0