A point moves such teat its distance from the point `(4,0)` is half that of its distance from the line `x=16 ,` find its locus.

Explanation

Let P(h, k) be the point and the given point is` A(4, 0)`.


We know that distance of the point` (x_1, y_1)` from the line `ax +by +c = 0` is


`d = (ax_1 + by_1 + c)/sqrt(a^2+b^2)->(i)`

By distance formula `AP=sqrt((h-4)^2+(k-0)^2)`

`AP = sqrt((h – 4)^2 + k^2)->(2)`


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