Question

The equation to the locus of a point which moves so that its distance from x-axis is always one half

its distance from the origin, is

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

Let the moving point be (x, y) and its distance from x - axis is y. Therefore, according to given condition

$\frac{1}{2}\sqrt{x^2+y^2}$ = y $\Rightarrow$ $x^2-3y^2=0$

This is required locus of the point (x, y).