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 the same distance of (h,k) from (2,4) and x-axis.

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

From distance formula:

Distance of (h,k) from (1,3) =

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

According to question both distances are same.

∴

Squaring both sides:

⇒

⇒

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

Thus, the locus of a point equidistant from (1,3) and x-axis is-

x² - 2x - 6y + 10 = 0 ….ans