If a +x b +y c = 0 , a b + b c + c a =6( b c ) , then the locus of the point (x, y) is

Step-by-step solution

Given, a +x b +y c = 0 As we know that, if a + b + c =0 Then, a b = b c = c a 0 Now, if a +x b +y c =0 Let x( a b )=x y( b c )=y( c a )= p a b = p x , b c = p x y and c a = p y a b + b c + c a = p x + p x y + p y = p ( x+y+1 x y ) aligned & = ( x+y+1 x y ) x y ( b c ) & =(x+y+1)( b c ) aligned Comparing it with 6( b c ) , aligned & x+y+1=6 & x+y=5 & x+y-5=0 & aligned Hence, option (b) satisfies it.