Answer :

**Key points to solve the problem:**

• **Idea of distance formula-** Distance between two points A(x_{1},y_{1}) and B(x_{2},y_{2}) 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-

**x ^{2} - 2x - 6y + 10 = 0 ….ans**

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