SOLUTION: I'm really struggling with these types of problems. Find the equation of the parabola with the given information, then find the two points that define the latus rectum. Focus(-5

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: I'm really struggling with these types of problems. Find the equation of the parabola with the given information, then find the two points that define the latus rectum. Focus(-5      Log On


   

Question 1031488: I'm really struggling with these types of problems.
Find the equation of the parabola with the given information, then find the two points that define the latus rectum.
Focus(-5,-4) and directrix x =3.
I think what I mostly need help with is finding the vertex so I can use that info to find the equation. I'm not sure I understand how to find the vertex. Thank you.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
If the directrix is x=3, then you learn that the parabola opens to the left.
The distance from the focus to vertex is equal to the distance from vertex to directrix.
V%5Bx%5D-%28-5%29=3-V%5Bx%5D
V%5Bx%5D%2B5=3-V%5Bx%5D
2V%5Bx%5D=-2
V%5Bx%5D=-1
The y coordinate of the vertex is equal to the y coordinate of the focus.
(-1,-4)
%28x%2B5%29%5E2%2B%28y%2B4%29%5E2=%28x-3%29%5E2
%28x%5E2%2B10x%2B25%29%2B%28y%2B4%29%5E2=x%5E2-6x%2B9
-16x-16=%28y%2B4%29%5E2
-16x=%28y%2B4%29%5E2%2B16
x=-%28y%2B4%29%5E2%2F16-1