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

Explanation

Let `(x, y)` be the unknown point. Its distance from y-axis is `|x|`. It's distance from `(2,4)` is given by
`d=((x−2) ^2 +(y−4) ^2) ^(1/2)`

Now put `d=∣x∣`, since point is equidistant from the given point and y-axis.

`abs(x)=((x−2) ^2 +(y−4) ^2) ^(1/2)`

`x ^2 =x ^2 −4x+4+(y−4)^
2`

`(y−4) ^2 −4x+4=0`

So, the locus of the given point is parabola.