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# Find the locus of a point which is equidistant from (1, 3) and x-axis.

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

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