Question

What is the equation of the locus of a point which moves such that $4$ times its distance from the $x$-axis is the square of its distance from the origin?

• A. $x^2+y^2-4y=0$
• B. $x^2+y^2-4\left|y\right|=0$
• C. $x^2+y^2-4x=0$
• D. $x^2+y^2-4\left|x\right|=0$

Answer 1

The correct option is B $x^2+y^2-4\left|y\right|=0$

Let the point be given by $(h,k)$

According to the given condition, $4|k|=h^2+k^2$

Replacing $h$ by $x$ and $k$ by $y$, we get the required locus as $x^2+y^2-4|y|=0$