Question 192148This question is from textbook
: Find the vertex, focus and directrix of the parabola. [NOTE: fractions must be reduced and mixed numbers have to be reported as improper fractions]
y2 - 18y - 9x - 81 = 0
This question is from textbook
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Find the vertex, focus and directrix of the parabola. [NOTE: fractions must be reduced and mixed numbers have to be reported as improper fractions]
y^2 - 18y - 9x - 81 = 0
------
Complete the square on the y-terms:
y^2 - 18y + ? = 9x + 81+?
y^2 - 18y + 81 = 9x + 81 + 81
(y-9)^2 = 9(x + 18)
---
Vertex = (-18,9)
4p = 9
p = 9/4
-----------------
The parabola opens to the right.
The directrix is x = -18-(9/4) = -20 1/4
---------------
The focus is (-18+ (9/4), 9) = (-15 3/4 , 9)
=================================================
Cheers,
Stan H.
|
|
|
