Key points to solve the problem:

• Idea of distance formula- Distance between two points A(x₁,y₁) and B(x₂,y₂) is given by- AB =

How to approach: To find the locus of a point we first assume the coordinate of the point to be (h, k) and write a mathematical equation as per the conditions mentioned in the question and finally replace (h, k) with (x, y) to get the locus of the point.

Let the coordinates of a point whose locus is to be determined to be (h, k)

As we need to maintain a distance of (h,k) from origin such that it is 3 times the distance from the x-axis.

So we select a point (h,0) on the x-axis.

From distance formula:

Distance of (h,k) from (0,0) =

Distance of (h,k) from (h,0) =

According to question both distances are same.

∴

Squaring both sides:

h² + k² = 9k²

⇒ h² = 8k²

Replace (h,k) with (x,y)

Thus, the locus of a point is x² = 8y² …….ans