SOLUTION: I need the following please: standard form for: x^2-4x-2y-8=0 vertex and focus of the following parabola: y^2+10y-x+3=0 find the equation of the directrix of the parabola:

Question 98399: I need the following please:
standard form for: x^2-4x-2y-8=0
vertex and focus of the following parabola: y^2+10y-x+3=0
find the equation of the directrix of the parabola: 4x^2-8x-2y-4=0
thanks for the help
I have worked them - just not sure

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
standard form for: x^2-4x-2y-8=0
2y = x^2-4x-8
y = (1/2)x^2-2x-4
------------------
vertex and focus of the following parabola: y^2+10y-x+3=0
x = y^2+10y+3
Complete the square on the y terms:
x-3+? = y^2+10y+?
y^2+10y+25 = x-3+25
(y+5)^2 = x+22
------------------
Vertex: (-22,-5)
4p=1 so p=1/4
The parabola opens to the right so
focus = (-22+(1/4),-5) = (-87/4,-5)
---------------------------------
find the equation of the directrix of the parabola: 4x^2-8x-2y-4=0
Divde thru by 2 to get:
2x^2-4x-y-2=0
y+2 = 2x^2-4x
y+2+2*? = 2(x^2-2x+?)
2(x^2-2x+1) = y+2+2
2(x-1)^2 = y+4
(x-1)^2 = (1/2)(y+4)
----------------
Vertex = (1,-4)
4p=(1/2)
p = 1/8
--------------
Parabola opens up so directrix is p below the vertex.
Directrix: y = -4-(1/8) = -33/8
================
Cheers,
Stan H.

RELATED QUESTIONS
I need to find the vertex, focus, directrix and axis of symmetry of the parabola:... (answered by lynnlo)

Write the vertex form for a parabola with the given characteristics. 1. vertex ( 0, 0) (answered by ewatrrr)

Find the vertex, focus and directrix of the parabola, {{{ y^2-10y+4x+25=0 }}} (answered by josgarithmetic)

Write the vertex form for a parabola with the given characteristics. 1. vertex ( 0, 0) (answered by lwsshak3)

Hello, I cannot figure out how to solve the following problem - sorry it's 3 steps! (answered by richwmiller)

I need your help please. 1. Write the equation in the form ax+by+c=0 A. Y=3x+1 B.... (answered by Alan3354,rothauserc)

In 1 and 2, do the following: a) Write the equation of the parabola in standard form. (answered by greenestamps)

i need to list the vertex, focus, and directrix of this parabola (x+2) =... (answered by lwsshak3)

Convert the equation to standard form by completing the square on x or y. Then find the... (answered by scott8148,terasse jade)