SOLUTION: The question states, write the standard equation for each conic given the following info. Parabola with a focus (-2,3) and a directrix x=2 how do i write the standard equati

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: The question states, write the standard equation for each conic given the following info. Parabola with a focus (-2,3) and a directrix x=2 how do i write the standard equati      Log On


   

Question 170145: The question states, write the standard equation for each conic given the following info.
Parabola with a focus (-2,3) and a directrix x=2
how do i write the standard equation with this given information?
Found 2 solutions by jim_thompson5910, stanbon:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
First we need to find the vertex:

X-coordinate of the vertex: Simply average the x coordinate of the focus (-2) with the directix (2) to get %28-2%2B2%29%2F2=0%2F2=0

So the x-coordinate of the vertex is x=0. This means that h=0

-------------------------------------------

Y-coordinate of the vertex: This value is equal to the y-coordinate of the focus. So the y-coordinate of the vertex is y=3. This means that k=3


So the vertex is (0,3)


Now that we have the vertex, we can use that to find the distance from the focus to the vertex.

Since the focus (-2,3) is 2 units from the vertex (0,3), this means that p=2

-------------------------------------------

Now let's find the equation:

Since the focus is (-2,3) and the directrix is x=2, this means that the parabola is opening to the left like this



Photobucket - Video and Image Hosting


-4p%28x-h%29=%28y-k%29%5E2 Start with the standard equation (for parabolas that open up to the left)


-4%282%29%28x-0%29=%28y-3%29%5E2 Plug in p=2, h=0, and k=3


-8%28x-0%29=%28y-3%29%5E2 Multiply


So the standard equation is -8%28x-0%29=%28y-3%29%5E2

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
write the standard equation for each conic given the following info.
Parabola with a focus (-2,3) and a directrix x=2
---------------
Plot the information you have so you can see what is happening.
The vertex is equidistanc from the directrix and the focus
so it must be at (0,3)
--------------------
p is the distance from the vertex to the focus; so p=-2.
Then 4p = -8
-------------------
Equation Form:
(y-k)^2 = 4p(x-h) where (h,k) is the vertex.
Your Equation:
(y-3)^2 = -8(x)
===========
Cheers,
Stan H.