If for [- 3 , 0 ] , the points (x, y)= (3 ( + 3 ), 2 ( + 6 ) ) lie on x y+ x+ y+ =0 , then ^2+ ^2+ ^2 is equal to :

Step-by-step solution

aligned & x=3 ( + 3 1- 3 ) & x- 3 =3 +3 3 & = x-3 3 3+ 3 x (1) & 2 ( + 1 3 1- 3 =y ) & 2( 3 +1)=y( 3 - ) . aligned using (1) and (2) aligned & 2 ( x-3 3 3 +x +1 )=y ( 3 - (x-3 3 ) 3 ( 3 +x) ) & 2 3 (x-3 3 +x+ 3 )=y(3( 3 +x)-x+3 3 ) & 4 3 x-12=y(2 x+6 3 ) & x y-2 3 x+3 3 y-6=0 & =-2 3 , =3 3 , =-6 & ^2+ ^2+ ^2=12+27+36=75 aligned