Given that \(A\) is the point \((0,3)\) and \(B\) is the point \((0,-3)\), a point \(P(x,y)\) moves so that \(PA=2PB\). Show that the equation of the locus of \(P\) is \[ x^2 + y^2 +10y + 9 = 0.\]
Geometry of Equations
Question
Given that \(A\) is the point \((0,3)\) and \(B\) is the point \((0,-3)\), a point \(P(x,y)\) moves so that \(PA=2PB\). Show that the equation of the locus of \(P\) is \[ x^2 + y^2 +10y + 9 = 0.\]