Question

Find the equation of the locus of a point whose distance from $(a,0)$ is $m$ times its distance from $(0,a)$

Answer 1

let the point be $(x,y)$

given that $\sqrt{(x-a{)}^2+(y-0{)}^2}=m\sqrt{(x-0{)}^2+(y-a{)}^2}$

locus will be $(m^2-1)x^2+(m^2-1)y^2-2ay{m}^2+2ax+(m^2-1)a^2=0$