if `a, b, c, a_1, b_1 and c_1` are non-zero complexnumbers satisfying `a/a_1+b/b_1+c/c_1=1+i and a_1/a+b_1/b+c_1/c=0,` where `i=sqrt-1,` the value of `a^2/a_1^2+b^2/b_1^2+c^2/c_1^2` is

If the points (a, b), (a_1, b_1) and (a-a_1 , b-b) are collinear, show that a/a_1 = b/b_1

If the points (a,b),(a_1,b_10 and (a-a_1,b-b_1) are collinear, show that a/a_1=b/b_1

For two linear equations , a_1x + b_1y + c_1=0 and a_2x + b_2y + c_2 = 0 , the condition (a_1)/(a_2)=(b_1)/(b_2)=(c_1)/(c_2) is for.

If ax^2+2bx+c=0 and a_1x^2+2b_1x+c_1=0 have commonroot and a/a_1,b/b_1,c/c_1 are in A.P., show that are: ax^2+2bx+c=0

If the points (a_1, b_1),\ \ (a_2, b_2) and (a_1+a_2,\ b_1+b_2) are collinear, show that a_1b_2=a_2b_1 .

If a^2+2bx+c=0 and a_1x^2+2b_1x+c_1=0 have a common root and a/a_1,b/b_1,c/c_1 are in AP then a_1,b_1,c_1 are in (A) A.P. (B) G.P. (C) H.P. (D) none of these

In direct proportion a_1/b_1 = a_2/b_2

If A_1,B_1,C_1, , are respectively, the cofactors of the elements a_1, b_1c_1, , of the determinant "Delta"=|a_1b_1c_1a_1b_2c_2a_3b_3c_3|,"Delta"!=0 , then the value of |B_2C_2B_3C_3| is equal to a1 2 b. a_1 c.a_1^2 d. a1 2^2

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 .