If the ordered pair satisfying the equations `a_1 x+b_1 y +c_1 and a_2 x + b_2 y +c_2` has 1 as its first coordinate, then which of the following is correct?

In the pair of linear equations a_1x+b_1y+c_1=0 and a_2x+ b_2y + C_2 = 0. If a_1/a_2 ne b_1/b_2 then the

Find the condition so that the two equations a_1 x^2+b_1 x+c_1=0 and a_2 x^2+b_2 x+c_2=0 will have a common root.

If the lines drawn to the linear equations of the type a_1 x+b_1 y+c_1=0 and a_2 x+b_2 y+c_2 =0 are coincident on each other, then the correct relation among the following is

If the line a_1 x + b_1 y+ c_1 = 0 and a_2 x + b_2 y + c_2 = 0 cut the coordinate axes in concyclic points, prove that : a_1 a_2 = b_1 b_2 .

If a_1/a_2!=b_1/b_2 then the system of equation a_1x+b_1y+c_1=0 , a_2x+b_2y+c_2=0 has

If a_1,b_1,c_1 and a_2,b_2,c_2 are the direction ratios of two lines , then write the condition of its perpendicularity.

(1) The straight lines (2k+3) x + (2-k) y+3=0 , where k is a variable, pass through the fixed point (-3/7, -6/7) . (2) The family of lines a_1 x+ b_1 y+ c_1 + k (a_2 x + b_2 y + c_2) = 0 , where k is a variable, passes through the point of intersection of lines a_1 x + b_1 y + c_1 = 0 and a_2 x+ b_2 y + c_2 = 0 (A) Both 1 and 2 are true and 2 is the correct explanation of 1 (B) Both 1 and 2 are true and 2 is not a correct explanation of 1 (C) 1 is true but 2 is false (D) 1 is false but 2 is true

(1) The straight lines (2k+3) x + (2-k) y+3=0 , where k is a variable, pass through the fixed point ( -3/7, -6/7) . (2) The family of lines a_1 x+ b_1 y+ c_1 + k (a_2 x + b_2 y + c_2) = 0 , where k is a variable, passes through the point of intersection of lines a_1 x + b_1 y + c_1 = 0 and a_2 x+ b_2 y + c_2 = 0 (A) Both 1 and 2 are true and 2 is the correct explanation of 1 (B) Both 1 and 2 are true and 2 is not a correct explanation of 1 (C) 1 is true but 2 is false (D) 1 is false but 2 is true

If the origin lies in the acute angle between the lines a_1 x + b_1 y + c_1 = 0 and a_2 x + b_2 y + c_2 = 0 , then show that (a_1 a_2 + b_1 b_2) c_1 c_2 lt0 .