SOLUTION: Find an equation of a parabola with a) focus (5,0) and directrix x = -5 b) focus (0,-7) and directrix y = 7 Can you please help me out? Thanks so much in advance:)

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Find an equation of a parabola with a) focus (5,0) and directrix x = -5 b) focus (0,-7) and directrix y = 7 Can you please help me out? Thanks so much in advance:)       Log On


   

Question 867542: Find an equation of a parabola with
a) focus (5,0) and directrix x = -5
b) focus (0,-7) and directrix y = 7
Can you please help me out? Thanks so much in advance:)

Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
I suggest using Distance Formula for this one and your other request post.

Use the definition for a parabola.

Unknown set of points, (x,y).
For question (a) of this posting,
The set of directrix points, a line, is (-5,y).
sqrt%28%28x-5%29%5E2%2B%28y-0%29%5E2%29=sqrt%28%28x-%28-5%29%29%5E2%2B%28y-y%29%5E2%29
sqrt%28%28x-5%29%5E2%2By%5E2%29=sqrt%28%28x%2B5%29%5E2%2B0%5E2%29
sqrt%28%28x-5%29%5E2%2By%5E2%29=sqrt%28%28x%2B5%29%5E2%29
Square both sides.
%28x-5%29%5E2%2By%5E2=%28x%2B5%29%5E2
You might not know by looking at it, but here, the x^2 terms will disappear.
x%5E2-10x%2B25%2By%5E2=x%5E2%2B10x%2B25
-10x%2B25%2By%5E2=10x%2B25
-20x%2B25%2By%5E2=25
-20x%2By%5E2=25
-20x=-y%5E2%2B25
20x=y%5E2-25
x=%281%2F20%29y%5E2-25%2F20
highlight%28x=%281%2F20%29y%5E2-5%2F4%29