# Use the definition of a parabola and the distance

1. Apr 20, 2010

### r-soy

Hi all

Use the definition of a parabola and the distance formula to find the equation of a parabola with

a ) directix x = -4 and focus (2,2 )
B ) directix x = 2 and focus (6,-4 )

How i solve like this queation please hle me the steps to solve that

thanks

2. Apr 20, 2010

### tiny-tim

Hi r-soy!
First, write out the definition of a parabola, and the distance formula …

what are they?

3. Apr 20, 2010

### r-soy

hhhh what is the formula ??

4. Apr 20, 2010

### tiny-tim

The "distance formula"?

I've no idea … you mentioned it.

5. Apr 20, 2010

### Staff: Mentor

Aww, I'll bet you're just being coy, tiny-tim.

6. Apr 20, 2010

### tiny-tim

uhh? oh, for a moment i thought you said "koi"!

no, i really don't know which formula is being referred to (i'll guess it has something to do with the focus or the directrix)

7. Apr 20, 2010

### Staff: Mentor

Here's the definition: A parabola is the set of all points equidistant from a fixed point (the focus) and a fixed line (the directrix).

The distance formula is the plain old distance formula we all know and love.

8. Apr 21, 2010

### tiny-tim

uhhh? do you mean Pythagoras?

9. Apr 21, 2010

### Susanne217

As I see it first the distance between the point (x,y) and (2,2) [The focus] can be expressed

$$\sqrt{(x-2)^2 + (y-2)^2} = 2+y$$

which can be simplified to to find the expression for the parabol in case a..

Which gives us

$$y = \frac{x^2-4x+4}{8}$$ as the expression for the parabola in case a).

Susanne

Last edited: Apr 21, 2010
10. Apr 21, 2010

### HallsofIvy

Staff Emeritus
Very good. However, I wonder if r-soy ever tried to do that, or if he even knows the definition of "parabola".

11. Apr 21, 2010

### Susanne217

If not there is magically place out there called The Google and The Wikipedia which can give the definition of both the parabola and how and why to use the formula which I used in the above post.

But I say thanks for the compliment HallsoftIvy. Now I will sleep well knowing that the great HallsoftIvy gave me a thumbs up for my work for once :D

Have a nice day...

I consider Pre-Calculus to be High School level Math. But some of problems posted in Pre-Calculus are like Post Calculus and even post-Real Analysis here. Is it because whats Pre-Calculus in one country isn't the same all over?

Last edited: Apr 21, 2010