S is the poin(4,0) and M is the foot of perpendicular drawn from point P to Y-axis .If P moves such that its distance Ps and PM remain equal ,find the locus of point P.hence identify

Explanation

in the question as `PS=PM`

let the coordinates of P,S & M be `(x_1,y_1) , (4,0), (0, alpha)` respectively.

PS = `sqrt((x_1 - 4)^2 + (y_1 - 0)^2)`

`PS= sqrt((x_1- 4)^2+ y_1^2 `

`PM = sqrt((x_1-0)^2 + (y_1 -alpha)^2)`

PM= `sqrt(x_1^2 + (y_1- alpha)^2)`

PS=PM

`sqrt((x_1-4)^2 + y_1^2) = sqrt(x_1^2 + (y_1 - alpha)^2)`

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