Question

The locus of a point which moves such that its distance from the point $(0,0)$ is twice its distance from the $Y$-axis, is

• A. $x^2 − y^2 = 0$
• B. $x^2 − 3y^2 = 0$
• C. $3x^2 − y^2 = 0$
• D. None of these

Answer 1

Answer: (C)

By hypothesis,
$\left| OP\right| = 2 \left |PM\right|$

$\Rightarrow \sqrt{x_{1}^{2}+y_{1}^{2}}=2\left| x_{1}\right|$
On squaring both sides, we get
$x_{1}^{2}+y_{1}^{2}=4 x_{1}^{2} \Rightarrow 3 x_{1}^{2}-y_{1}^{2}=0$
$\therefore $ Locus of the point is $3 x^{2}-y^{2}=0$