Question

Find the equation of locus of points whose distance from the point $(2,3)$ is twice its distance from $(1,2)$.

Answer 1

Let the point be $(x,y)$

Given that $\sqrt{(x-2{)}^2+(y-3{)}^2}=2\sqrt{(x-1{)}^2+(y-2{)}^2}$

Locus is $3x^2+3y^2-4x-10y+7=0$