a) [latex]S=(x,y)\ egin{cases} |SA|=|SB|\ |SA|=|SC| end{cases}\ egin{cases} sqrt{(x-1)^2+(y-0)^2}=sqrt{(x-0)^2+(y-2)^2}\ sqrt{(x-1)^2+(y-0)^2}=sqrt{(x-1)^2+(y-4)^2} end{cases}\ egin{cases} (x-1)^2 + y^2 = x^2+(y-2)^2\ (x-1)^2 + y^2 = (x-1)^2 + (y-4)^2 end{cases}\ egin{cases} x^2-2x+1+y^2 = x^2 + y^2 - 4y +4\ x^2-2x+1+y^2 =x^2-2x+1+y^2-8y+16 end{cases}\ egin{cases} -2x+1=-4y+4\ 0=-8y+16 end{cases}\ 8y=16\ y=2\ -2x+1=-4cdot 2+4\ -2x+1=-8+4\ -2x=-5\ x=2frac{1}{2}\ [/latex] [latex]S=(2frac{1}{2},2)\ r=|SA|\ r=sqrt{(2frac{1}{2}-1)^2+(2-0)^2}=sqrt{2frac{1}{4}+4}=sqrt{6,25}=2,5\ (x-a)^2+(y-b)^2=r^2\ (x-2frac{1}{2})^2 +(y-2)^2 = 6,25[/latex] b) [latex]S=(x,y)\ egin{cases} sqrt{(x-7)^2+(y+1)^2}=sqrt{(x-5)^2+(y-3)^2}\ sqrt{(x-7)^2+(y+1)^2}=sqrt{(x+1)^2+(y+5)^2} end{cases}\ egin{cases} x^2-14x+49+y^2+2y+1=x^2-10x+25+y^2-6y+9\ x^2-14x+49+y^2+2y+1=x^2+2x+1+y^2+10y+25 end{cases}\ egin{cases} -14x+2y+50=-10x-6y+34\ -14x+2y+50=2x+10y+26 end{cases}\ egin{cases} -4x+8y=-16\ -16x-8y=-24 end{cases}\ -20x = -40\ x=2\ -8 +8y = -16\ 8y = -8\ y=-1\ S=(2,-1)\ r=sqrt{(2-7)^2+(-1+1)^2}=sqrt{25}=5\ (x-2)^2+(y+1)^2=25 [/latex]
