SOLUTION: find the vertex, focus & directrix for the following functions: (y-4)^2 = 20(x-4) Vertex = ? focus = ? directrix x = ? y^2 - 86 = 12x

SOLUTION: find the vertex, focus & directrix for the following functions: (y-4)^2 = 20(x-4) Vertex = ? focus = ? directrix x = ? y^2 - 86 = 12x - 4^2 Vertex = ? focus = ? directr

Question 205837: find the vertex, focus & directrix for the following functions:
(y-4)^2 = 20(x-4)
Vertex = ?
focus = ?
directrix x = ?
y^2 - 86 = 12x - 4^2
Vertex = ?
focus = ?
directrix x = ?
(x-9)^2 = 12(y-5)
Vertex = ?
focus = ?
directrix x = ?
x^2 + 40x = 4y - 16
Vertex = ?
focus = ?
directrix x = ?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
find the vertex, focus & directrix for the following functions:
Form: (y-k)^2 = 4p(x-h)
Vertex: (h,k)
Focus: (h,k+p)
Directrix: x = h
--------------------------------
(y-4)^2 = 20(x-4)
Vertex = (4,4)
focus = (4,4+5)
directrix x = 4
-------------------------
y^2 - 86 = 12x - 4^2
(y-0)^2 = 12x +86 - 16
(y-0)^2 = 12(x+(70/12))
Vertex = (-70/12 , 0)
focus = (-70/12 , 3)
directrix x = -70/12
----------------------------
I'll leave this one to you.
(x-9)^2 = 12(y-5)
Vertex = ?
focus = ?
directrix x = ?
---------------------------------
x^2 + 40x = 4y - 16
x^2+40x+20^2 = 4y-16+20^2
(x+20)^2 = 4y+384
(x+20)^2 = 4(y+96)
Note: This parabola is opening to the right.
---
Vertex = (-20,-96)
focus = (-20+1 , -96)
directrix y = -96
==========================
Cheers,
Stan H.
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