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 +???
= (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!

asked by Nye
  1. 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

    posted by Steve

Respond to this Question

First Name

Your Response

Similar Questions

  1. 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 +??? = (x-2)2 + (y-3)2 +??? I tried solving it using the distance
  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
  3. 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
  4. Add math

    P(x,y) moves such that its distance from point Q(4,8)is twiceits distance from point P(-2,3). Find the equation of the locus of moving point P.
  5. Admaths

    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.
  6. 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!!
  7. add maths

    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.
  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. math

    I need help with parametric equations, locus problems, tell me how to solve all questions if you can. Need help with one below: Tangents are drawn to a parabola x^2=4y from an external point A(x1,y1) touching the parabola at P and
  10. 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.

More Similar Questions