Question

The locus of a point,which moves in such a way that its distance from from the origin $(0,0)$ is thrice the distance from $x$ axis is ?

• A. $x^2-8y^2=0$
• B. $4x^2-y^2=0$
• C. $x^2+8y^2=0$
• D. $x^2-4y^2=0$

Answer 1

The correct option is A $x^2-8y^2=0$

Let the point be $(h,k)$.
Distance from origin: $\sqrt{h^2+k^2}$
Distance from x-axis: $|k|$
Given:
$\sqrt{h^2+k^2}=3|k|$
Squaring both sides:
$h^2+k^2=9k^2$
$⟹h^2-8k^2=0$
Replacing $(h,k)=(x,y)$ gives the required locus:
$x^2-8y^2=0$