If a point P moves such that its distances from the point A(1,1) and the line x+y+2=0 are equal, then the locus of P is

Step-by-step solution

Let the co-ordinates of P are (x, y) According to given condition aligned & (x-1)^2+(y-1)^2= (x+y+2)^2 2 & 2 (x^2+1-2 x )+2 (y^2+1-2 y ) & =x^2+y^2+4+2 x y+4 y+4 x aligned On comparing with aligned & a x^2+b y^2+2 h x y+2 g x+2 f y+c=0 , we get & a=1, b=1, h=-1, g=-4, f=-4, c=0 & a b c+2 f g h-a f^2-b g^2-c h^2 & =1.1 .0+2(-4)(-4)(-1)-1(-4)^2-1(-4)^2-0 & =0-32-16-16=-64 0 & and h^2-a b=1-1=0 & Since 0 and h^2=a b , & aligned therefore locus of P is a parabola.