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