Question 986443
You are saying Distance between (x,y) and B(0,3)  is 2 times distance between (x,y) and O(0,0).  You are expecting, according to description, the points (x,y) are a circle.


{{{sqrt((x-0)^2+(y-3)^2)=2*sqrt((x-0)^2+(y-0)^2)}}}
{{{sqrt(x^2+(y-3)^2)=2sqrt((x)^2+(y)^2)}}}
{{{x^2+(y-3)^2=4(x^2+y^2)}}}
{{{x^2+(y-3)^2=4x^2+4y^2}}}
{{{x^2+y^2-6y+9=4x^2+4y^2}}}
{{{-6y+9=3x^2+3y^2}}}
{{{-2y+3=x^2+y^2}}}
{{{x^2+y^2+2y=3}}}
Want standard form, requiring Completing the Square
{{{x^2+y^2+2y+1=3+1}}}
{{{highlight(x^2+(y+1)^2=4)}}}
Circle, centered at <b>(0,-1)</b>, and radius is {{{sqrt(4)=highlight(2)}}}.