Question

Locus of a point which moves so that its distance from the origin is thrice its distance from $x$ axis is

• A. a straight line
• B. a pair of straight lines
• C. a circle
• D. a parabola

Answer 1

The correct option is A a straight line

Let point be $P(x,y)$

According to question distance from the origin is thrice the distance from $x-axis$. So,

$\sqrt{x^2+y^2}=3y$

$⟹x^2+y^2=9y^2$...........[squaring both sides]

$⟹x^2=8y^2$

Hence, $x=\sqrt{8}y$ or $x=-\sqrt{8}y$.........[equation of straight lines]