Ask Experts Questions for FREE Help !
Ask
    Curtis1993's Avatar
    Curtis1993 Posts: 4, Reputation: 1
    New Member
    		  
    #1

    Aug 8, 2009, 02:14 PM
    find equation of parabola with vertex and focus
    What is the equation of the parabola with vertex (-1,3) and focus (1,3)? I need an explanation please.
    galactus's Avatar
    galactus Posts: 2,271, Reputation: 282
    Ultra Member
    		  
    #2

    Aug 8, 2009, 03:08 PM
    The distance between the focus and the vertex is designated by p.

    The vertex coordinates are (h,k)=(-1,3).

    If a parabola opens in the positive x direction as this one does, its equation is given by



    It is easy to see that the distance between the focus and vertex, p, is 2 because the distance from x=1 to x=-1 is 2 units.

    Plug in p, h,k and solve for x.

    Oh yeah, another thing in case you need it. The directrix is a vertical line in front of the vertex the same distance from the vertex as the focus.

    Therefore, the directrix would be at x=-3

    See, here is what a parabola actually is. All points on the parabola are the same distance from the focus as they are from the directrix.

    Draw a line from the focus to anywhere on the parabola. Then, from that point draw straight to the directrix. The distances are the same.
    Attached Images
     
    Curtis1993's Avatar
    Curtis1993 Posts: 4, Reputation: 1
    New Member
    		  
    #3

    Aug 8, 2009, 03:53 PM

    Thank you for all of your help galactus. I have a better understanding, but in your diagram you show v as 1,3 not -1,3 was this just a typo. Also, what would I plug in for y? Thank you for your help.
    galactus's Avatar
    galactus Posts: 2,271, Reputation: 282
    Ultra Member
    		  
    #4

    Aug 8, 2009, 03:55 PM
    Yes, duh, that should be F(1,3). A typo.

    You do not plug in anything for y. The parabola lies on its side, so it is in terms of y instead

    of x. When you solve for x, you have something of the form

    a, b, and c will be determined when you solve for x. That is just a general form.

    If my response helps, please 'rate this answer' for me. That's all I ask.:)
Not your question? Ask your question View similar questions
 

Question Tools Search this Question
Search this Question:

Advanced Search


Check out some similar questions!

Find vertex, axis, focus, p, directrix of conic equation [ 8 Answers ]

-4(y+2) = (x-3)^2 I need help finding the vertex, axis, p, focus, and directrix. I'm so blanked out.I cannot remember anything.

Find the vertex, focus, and directrix of the parabola given by the equation. [ 1 Answers ]

(x-9)^2=-(y+8)?

Find equation of a parabola given the vertex and directrix [ 1 Answers ]

What is the equation of a parabola with a vertex at (4,8) and a directrix at y=5? I calculated the distance from the vertex to the directrix as p=3. my answer key says p=6. I cannot see were I went wrong. Can anyone provide some guidance? If p=3 is correct then the equation would be: ...

Find vertex, parabola, directrix of the parabola equation [ 1 Answers ]

Find the Vertex, Focus, Directrix of the parabola equation: x-(y^2)+4y-2=0

I need to find the distance from the focus to the vertex of a parabola [ 1 Answers ]

My question is how can I find the distance from the focus to the vertex of a parabola with the given equation y^2=-10x. Can someone please explain and help me with the answer??

View more questions Search