SOLUTION: AH peoplle please help im stuck on these!! ahh :( it says Determine an equation of the parabola with the following property 1) Focus at (0,-6) and directrix y=6.

Question 70893: AH peoplle please help im stuck on these!!
ahh
:(

it says Determine an equation of the parabola with the following property
1) Focus at (0,-6) and directrix y=6.

THEN it says
determine the vertex,focus,and directrix for each parabola. Sketch each parabola.
1) y[squared]=-3x
2)x[squared]=12y
3) x[squared]-8x-y+20=0

oh man please help anyone! :(
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Determine an equation of the parabola with the following property
1) Focus at (0,-6) and directrix y=6.
Plot the point and sketch the line on a coordinate system.
The vertex is half way between the directrix and the focus.
So the vertex is (0,0)
"p" is the distance from the vertex to the focus:
p=-6
Therefore 4p=-24
So the equation of the parabola is:
(x-0)^2 = -24(y-0)
x^2 = -24y
y=(-1/24)x^2
--------------------
THEN it says
determine the vertex,focus,and directrix for each parabola. Sketch each parabola.
1) y[squared]=-3x
Put the equation in vertex form which is (y-k)^2 = 4p(x-h)
(y-0)^2 = -3(x-0)
vertex is (0,0)
4p = -3
p = -3/4
So the focus is at (-3/4,0)
The directrix is x=3/4
----------------
2)x[squared]=12y
(x-0)^2 = 12(y-0)
vertex = (0,0)
4p=12
p=3
Focus is at (0,3)
Directrix is y=-3
-----------------------
3) x[squared]-8x-y+20=0
x^2-8x = y-20
Complete the square to get:
x^2-8x+16 = y-20+16
(x-4)^2 = y-4
vertex at (4,4)
4p = 1
p= 1/4
Focus (4,4+1/4) or (4,17/4)
directrix at y=4-(1/4)
y=15/4
--------------
Cheers,
Stan H.
RELATED QUESTIONS
ah help meeeeeee :[[ it says determine whether each parabola opens upward,downward,left... (answered by stanbon)

im stuck on a geometry problem, the problem says "find the value of the variable." then... (answered by CharlesG2)

please help with the following question i just cant figure it out it says Find the three (answered by stanbon)

Please help me with problem. It says to Simplify this expression. And im doing... (answered by tutorcecilia)

Hello i really need help on a wriiten equation im not good on those it says open ended ,... (answered by nyc_function)

please help me with this equation. i did the distributive property and i think im doing... (answered by persian52,dabanfield,cornball3440,JBarnum)

Please help me! Cannot figure this out. it says: without drawing the graph of the given... (answered by josmiceli)

Im studying right now in College Algebra... parallel and perpendicular lines I'm stuck... (answered by lwsshak3)

Im in algebra II but we are going over algebra 1 a bit before we start. Im stuck on a... (answered by Alan3354)