|
Question 285165: The question is : Identify the vertex, focus, axis of symmetry, and directrix for the parabola whose equation is y^2– 8y + 16x– 64 = 0.
I tried completing the square, but I only got more confused. My textbook does not say what the directrix is or how to identify it or the focus, axis of symmetry, or the vertex as well. It mentions them, but does not show the process of finding them. Could you explain it?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! The question is : Identify the vertex, focus, axis of symmetry, and directrix for the parabola whose equation is y^2– 8y + 16x– 64 = 0.
I tried completing the square, but I only got more confused. My textbook does not say what the directrix is or how to identify it or the focus, axis of symmetry, or the vertex as well. It mentions them, but does not show the process of finding them. Could you explain it?
--------------------------------------
Completing the Square:
y^2-8y + ? = -16x + 64 + ?
----
y^2 - 8y + 16 = -16x + 64 + 16
----
(y-4)^2 = -16x + 80
----
-16x = (y-4)^2 - 80
x = (-1/16)(y-4)^2 + 5
---------------------------------
This is a parabola opening to the left.
---
Vertex: (5,4)
---
Axis: y = 4
-------
Directrix?
4p = -1/16
p = -1/64
Directrix is x = 5+(1/64)
===============================
Cheers,
Stan H.
|
|
|
| |
