The equation of the locus of the point whose distance from x-axis is twice its distance from the y-axis is

Let $P\left(x_1,y_1\right)$ be any point on required locus. 

Given that the distance from x-axis is twice its distance from the y-axis

The distance from the point $P\left(x_1,y_1\right)$ to $x-$ axis is $\left|y_1\right|$ and the distance between from the point to $y-$ axis is $\left|x_1\right|$

Given that the distance from  p to x-axis is twice its distance from the y-axis

$$\begin{gathered} \Rightarrow \left|y_1\right|=2\left|x_1\right| \\ squaring on both sides \\ {y^2}_1=4{x^2}_1 \\ \therefore locus of p(x_1 ,y_1) is y^2=4x^2 \end{gathered}$$