Question

Find the equation of the locus of a point whose distance from the x-axis is half its distance from the
origin.​

Answer 1

Answer:

The locus of is the union of the straight lines $((3^{0.5}x-y)=0  and   ((3^{0.5}x+y) =0$.

Step-by-step explanation:

Let the coordinate of the locus is (x,y) that is the distance from y axis is |x|.

As given the distance from the origin is $|x|=(x^{2} +y^{2} )^{\frac{1}{2} }\\hence, 4x^{2} =x^{2} +y^{2} \\\\and, ((3^{0.5}x-y) ((3^{0.5}x+y) =0$

Therefore the locus of is the union of the straight lines $((3^{0.5}x-y)=0  and   ((3^{0.5}x+y) =0$.