Let `a,b,c in R` such that `a^(2)+b^(2)+c^(2)=2bc,a^(2)+b^(2)+c^(2)!=0`. Then which of the following points lie on the line `ax+by+c=0`, is :
(A) `(-1,2)` (B) `(1,2)` (C) `(-1,-2)` (D) `(2,-1)`

(i ) If the length of perpendicular from origin to the line ax+by+a+b=0 is p , then show that : p^(2)-1=(2ab)/(a^(2)+b^(2)) (ii) If the length of perpendicular from point (1,1) to the line ax-by+c=0 is unity then show that : (1)/(a)-(1)/(b)+(1)/(C )=(c )/(2ab)

If [[a,a^(2),a^(3)-1b,b^(2),b^(3)-1c,c^(2),c^(3)-1]]=0

If a!=b!=c such that |[a^3-1,b^3-1,c^3-1] , [a,b,c] , [a^2,b^2,c^2]|=0 then

Let a,b,c,d,a in R and satify the relations a(b-c)^(2)+a_(1)bc=c-0 and a(b+c_(1))^(2)+a_(2)bc_(1)+c=1 then which is true

Let a,b and c be such that a+b+c=0 and P=(a^(2))/(2a^(2)+bc)+(b^(2))/(2b^(2)+ca)+(c^(2))/(2c^(2)+ab) is defined.What is the value of P?[1]

If a, b, c, d are in GP, then prove that 1/((a^(2)+b^(2))), 1/((b^(2)+c^(2))), 1/((c^(2)+d^(2))) are in GP.

If a+b+c =0, then the value of frac(a^2 +b^2+c^2) (a^2 - bc) is (A) 0 (B) 1 (C) 2 (D) 3

Prove that det[[1,a,a^(2)-bc1,b,b^(2)-ca1,c,c^(2)-ab]]=0