If the equation `(a_1-a_2)x+(b_1-b_2)y=c` represents the perpendicular bisector of the segment joining `(a_1,b_1)(a_2,b_2),` then `2c =`

In direct proportion a_1/b_1 = a_2/b_2

If (b_2-b_1)(b_3-b_1)+(a_2-a_1)(a_3-a_1)=0 , then prove that the circumcenter of the triangle having vertices (a_1,b_1),(a_2,b_2) and (a_3,b_3) is ((a_2+a_3)/(2),(b_2+b_3)/(2)) .

If (b_2-b_1)(b_3-b-1)+(a_2-a_1)(a_3-a_1)=0 , then prove that the circumcenter of the triangle having vertices (a_1,b_1),(a_2,b_2) and (a_3,b_3) is ((a_2+a_3)/(2),(b_2+b_3)/(2)) .

If (b_2-b_1)(b_3-b_1)+(a_2-a_1)(a_3-a_1)=0 , then prove that the circumcenter of the triangle having vertices (a_1,b_1),(a_2,b_2) and (a_3,b_3) is ((a_2+a_3)/2,(b_(2+)b_3)/2)

Delta=|{:(a_1,b_1,c_1),(a_2,b_2,c_2),(a_3,b_3,c_3):}|and Delta'|{:(A_1,B_1,C_1),(A_2,B_2,C_2),(A_3,B_3,C_3):}| where A_1,B_1,C_1,A_2,B_2,……… are respectively the cofactors of the elements a_1,b_1,c_1,a_2,b_2,….. of the determinant then Delta'=........

If (a_1)/(a_2)=(b_1)/(b_2)=(c_1)/(c_2) then the lines are………lines.

If the line a_1x+b_1y=1,a_2x+b_2y=1,a_3x+b_3y=1 are concurrent then the points (a_1,b_1),(a_2,a_2),(a_3,b_3) ,

If the equation of the locus of a point equidistant from the points (a_1,b_1) and (a_2,b_2) is (a_1-a_2)x+(b_1-b_2)y+c=0 , then the value of C is

If the equation of the locus of a point equidistant from the points (a_1, b_1) and (a_2, b_2) is (a_1-a_2)x+(b_1-b_2)y+c=0 , then the value of c is

If the equation of the locus of a point equidistant from the points (a_1,b_1) and (a_2,b_2) is (a_1-a_2)x+(b_2+b_2)y+c=0 , then the value of C is