Thread: Parabola help

This is for review and I can't remember this.

What is the equation of a parabola with focus (6, -10) and directrix x = -2?

Originally Posted by Alan

This is for review and I can't remember this.

What is the equation of a parabola with focus (6, -10) and directrix x = -2?

Personally I prefer the long way (no surprise to anyone who knows me). A parabola is defined as the locus of points such that the distance between the focus and parabola is the same as the distance between the parabola and the directrix. So


-Dan

The answers I have to choose from are:

(y+10)^2 = 16(x-2)
(y+4)^2 = 16(x-6)(y-10)^2 = 16(x+2)
(y-4)^2 = 16(x+6)

I'm still kind of confused...

Originally Posted by Alan

This is for review and I can't remember this.

What is the equation of a parabola with focus (6, -10) and directrix x = -2?

See this.

I prefer the definition I used because I can get equations for parabolas with axes of symmetry that aren't "nice."

In any event the directrix here is parallel to the y axis, so we can use the form


p is the twice the distance between the directrix and the focus, so p = 4. The vertex is half way between the directrix and the focus so it is at V(2, -10). So the equation will be


Finally, we know that the focus is to the right of the directrix, so this parabola opens to the right. Thus we choose the + sign:


Edit:
You can solve for the answer using my method:










-Dan

I read the wiki page and tried to understand you but how do you get

Now square both sides



Transpose to the right side of the equation and expand the binomials and simplify.



The right side simplifies to



Factor out 16 on the right side