Question

A point moves so that its distance from the origin is always twice its distance from the point $(3,0)$. Its locus is

• A. a circle
• B. an ellipse
• C. a hyperbola
• D. a straight line
• E. a parabola

Answer 1

The correct option is A a circle

Let the point be $(x,y)$
Given that distance from origin is twice the distance from point $(3,0)$
We get $x^2+y^2=2{(x-3)}^2+2y^2$
Which implies $x^2+y^2-12x+18=0$
It represents a circle.