Equation of a parabola

R

Ryan Rigdon

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Joined
Jun 10, 2010
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I have tried to do this problem over and over again but getting nowhere. here is the problem. after the problem i will explain what i know and have currently.

Problem:
Find the equation of a parabola with vertex (4,1) and focus (4,-1).

Since both x values from the vertex and focus are the same, we have a vertical parabola.

Our vertical line @ x=4

standard equation of a v.p. is x^2 = 4py

vertex is @ (0,0) not (4,1). p=?


Now i know that the value of p can be negative with that said.

since both x's are at 4. we need to subtract the y of focus from y of vertex.

p=1--1=-2? (is this correct?)
 
Can you find the Directrix? It's an eyeball problem...
 
the rest of my work on this problem.


with p=2

x^2 = 8y

(x-a)^2 = 8(y-b) with vertex of (4,1)

a = 4 b = 1

(x-4)^2 = 8(y-1) is the equation of our parabola.
 
Pretty good, but you'll have to figure out why you did not get -8.

You didn't answer my question about the Directrix, either. The Directrix will help you avoid the sign error.
 
Knowing that, let's see you try to quit while you still have +8 going on in there.
 
Well, +8 suggests opening UP. With that Directrix up there, that will not do. Try -8.
 
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