If a point P moves such that the sum of the distances from P to the point A(1,-1) and B(-1,1) is always 4 , then the equation for the locus of P is

Step-by-step solution

Let point P(x, y) , so aligned & (x-1)^2+(y+1)^2 + (x+1)^2+(y-1)^2 =4 & (x-1)^2+(y+1)^2+(x+1)^2+(y-1)^2 & +2 (x-1)^2+(y+1)^2 (x+1)^2+(y-1)^2 =16 & 2 (x^2+y^2+2 )+2 (x-1)^2+(y+1)^2 & (x+1)^2+(y-1)^2 =16 & (x^2+y^2+2 )+ (x-1)^2+(y+1)^2 & (x+1)^2+(y-1)^2 =8 & [(x-1)^2+(y+1)^2 ] [(x+1)^2+(y-1)^2 ] & = (6-x^2-y^2 )^2 & [x^2+y^2-2 x+2 y+2 ] [x^2+y^2+2 x-2 y+2 ] & = (x^2+y^2-6 )^2 & aligned aligned & (x^2+y^2+2^2-4(x-y)^2= (x^2+y^2-6 )^2 . & [ (x^2+y^2+2 )- (x^2+y^2-6 ) ] & [ (x^2+y^2+2 )+ (x^2+y^2-6 ) ] & =4(x-y)^2 & 8 (