SOLUTION: A point P(x,y) moves so that its distance from the point K(2,5) is twice its distance from the line x=-1. Find the equation of the locus of P.

Question 1132430: A point P(x,y) moves so that its distance from the point K(2,5) is twice its distance from the line x=-1. Find the equation of the locus of P.
Answer by MathLover1(20849) (Show Source): You can put this solution on YOUR website!
The distance from (,) to the line will taken from
the perpendicular distance as shortest which will be a horizontal distance since is a vertical line.
This distance will be the difference in the coordinates
stated as a positive or =>

Since we want the distance from (,) to (,) to be
twice the distance from (,) to we have:

... square both sides
Note that since squaring will automatically result in a positive we will no longer need the absolute value sign.

Note this is becoming the equation of a hyperbola.
We want standard form :
We need to do some complete the square work here.

We have a hyperbola centered at (,) or (,).=>the equation of the locus of

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