If the sum of the distances from a variable point P to the given points A ( 1 , 0 ) and B ( 0 , 1 ) is 2 , then the locus of P is

Step-by-step solution

It is given that, A P + B P = 2 Consider the point P be   ( x ,   y ) . ( x - 1 ) 2 + y 2 + x 2 + ( y - 1 ) 2 = 2 ⇒ ( x - 1 ) 2 + y 2 = 2 - x 2 + ( y - 1 ) 2 Squaring on both sides, ( x - 1 ) 2 + y 2 = 4 + x 2 + ( y - 1 ) 2 - 4 x 2 + ( y - 1 ) 2 ⇒ x 2 + y 2 + 1 - 2 x = 4 + x 2 + y 2 + 1 - 2 y - 4 x 2 + ( y - 1 ) 2 ⇒ 2 y - 2 x = 4 - 4 x 2 + ( y - 1 ) 2 ⇒ y - x - 2 = - 2 x 2 + ( y - 1 ) 2 Squaring both the sides, x 2 + y 2 + 4 - 2 x y + 4 x - 4 y = 4 x 2 + 4 y 2 + 4 - 8 y ⇒ 3 x