# Math

posted by Nye

Let A(2,3) be a fixed point. A point P moves such that PA is equal to the distance of P from the y-axis. Find the equation of the locus of P

PA2 = (x-x1)^2 + (y-y1)^2 +???
= (x-2)^2 + (y-3)^2 +???

I tried solving it using the distance formula but I'm still confused because I am given only one point A (2,3) coordinate. I searched all blogs on google but couldn't find a solved problem similar to this. Please help!

1. Steve

Ths distance of (x,y) from the y-axis is just x. So,

√((x-2)^2 + (y-3)^2) = x
(x-2)^2 + (y-3)^2 = x^2
x^2-4x+4 + (y-3)^2 = x^2
(y-3)^2 = 4x-4
(y-3)^2 = 4(x-1)

as I showed using the properties of parabolas

## Similar Questions

1. ### Analytic Geometry

Find the equation of a locus of a point which moves so that the sum of its distance from (2,0)and (-2,0) is 8. it is about equation of a locus.. please help!!
2. ### Maths

Find the equation of the locus of the point P(x,y) which moves so that it's distance from the point (0,3) is equal to its distance from the line y=-3 Show that the point (-6,3) lies on the locus Please help me with thisand also show …

A point moves such that its distance from point A(1,0) is twice its distance from B(-2,0).Find the equation of the locus of the point.

A point Y moves such that its distance from point B (1,2) is constant. Given that x=k is the tangent of the locus of Y , express the equation of the locus in terms of k.
5. ### Pre-calculus

Find the equation of the locus of the point which moves so that its distance from the point (2,0) is 2/3 its distance from the line y=5.
6. ### Math

Let A(2,3) be a fixed point. A point P moves such that PA is equal to the distance of P from the y-axis. Find the equation of the locus of P PA2 = (x-x1)2 + (y-y1)2 +?
7. ### algebra

Find the equation for the graph of the path of a point​ P(x,y) that moves such that​ P(x,y) is the same distance from the point ​(14​,0) and the​ y-axis.
8. ### math

The locus of a point whose distance from point (0,5) is always 3/4 of its distance from the line Y=8 is an elipse. Find the equation,centre, length of the major axis, length of the minor axis and the foci of the ellipse.
9. ### co-ordinate geometry

S is the point (4,0) and M is the foot of the perpendicular drawn From a point to the y-axis.If P moves such that the distance PS and PM remain equal,find the locus of point P