# 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

Relevance

- PopeLv 74 years agoBest 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 sLv 74 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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