Find an equation for the collection of points for which the distance to (3, 0) is twice the distance to the line x = -3?

If the form is in:

((x-h)^2)/(p^2) - ((y-k)^2)/(q^2) = 1

What are:

h =

k =

p^2 =

q^2 =

Thank you

2 Answers

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  • Pope
    Lv 7
    4 years ago
    Best Answer

    It will be a hyperbola with eccentricity 2. Let P(x, y) be a point on the locus, F(3, 0) be the focus, and Q(-3, y) be the projection of P onto the given directrix.

    PF = 2PQ

    √[(x - 3)² + y²] = 2|x + 3|

    (x - 3)² + y² = 4(x + 3)²

    x² - 6x + 9 + y² = 4x² + 24x + 36

    -3x² - 30x + y² = 27

    -3(x² + 10x) + y² = 27

    -3(x² + 10x + 25) + y² = 27 - 3(25)

    -3(x + 5)² + y² = -48

    (x + 5)²/16 - y²/48 = 1

    h = -5

    k = 0

    p = 4

    q = 4√(3)

  • ted s
    Lv 7
    4 years ago

    given that [ (x - 3)² + y² ] = 4 [ (x + 3)² + y² ]...do the algebra.......d1 = 2 d2 ---> d1² = 4 d2²

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