Find the locus of a point equidistant from the point (2, 4) and the y-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 y-axis.


So we select a point (0,k) on the y-axis.


From distance formula:


Distance of (h,k) from (2,4) =


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


According to question both distances are same.



Squaring both sides:





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


Thus, the locus of point equidistant from (2,4) and the y-axis is-


y2 - 4x - 8y + 20=0 ….ans


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