SOLUTION: Hello! I need help with the following question. Graph the following parabola: (x-3)^2=8(y+5). I only know how to find the vertex ( 3,5) and p which is 2. But I do not know how to

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Question 1072507: Hello! I need help with the following question.
Graph the following parabola:
(x-3)^2=8(y+5). I only know how to find the vertex ( 3,5) and p which is 2. But I do not know how to find the focus and the directrix.
Thank you!
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39616)   (Show Source): You can put this solution on YOUR website!
The form in which your equation is written gives the information to find the focus and directrix. These examples will give the guidance to use:


Deriving equation for parabola given Focus and Directrix

different oriented and vertex not at the Origin, another deriving equation for parabola given focus and directrix
Answer by MathTherapy(10551)   (Show Source): You can put this solution on YOUR website!

Hello! I need help with the following question.
Graph the following parabola:
(x-3)^2=8(y+5). I only know how to find the vertex ( 3,5) and p which is 2. But I do not know how to find the focus and the directrix.
Thank you!
First of all, you have to determine whether the parabola has a vertical or horizontal axis.

This one has a vertical axis, so you compare the given equation to the standard-form equation, as follows:

 ----- Given equation

 ----- Standard-form equation of a parabola with a vertical axis, with (h, k) being the vertex

You have the vertex, or (h, k) as (3, 5), but the vertex, or 

As seen, 4p = 8, so  

Focus:      

Directrix:  

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