SOLUTION: Find the standard form of the equation of the parabola with a focus at (0, -3) and a directrix at y = 3. (5 points) y2 = -12x y2 = -3x y = negative 1 divided by 12 x2

Algebra ->  Trigonometry-basics -> SOLUTION: Find the standard form of the equation of the parabola with a focus at (0, -3) and a directrix at y = 3. (5 points) y2 = -12x y2 = -3x y = negative 1 divided by 12 x2      Log On


   

Question 1138078: Find the standard form of the equation of the parabola with a focus at (0, -3) and a directrix at y = 3. (5 points)

y2 = -12x

y2 = -3x

y = negative 1 divided by 12 x2

y = negative 1 divided by 3 x2
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!


The standard form is %28x+-+h%29%5E2+=+4p+%28y+-+k%29, where the focus is (h, k+%2B+p) and the directrix is y+=+k+-+p.

given:
a focus at (0, -3) =>(h, k+%2B+p)=(0, -3)
so, h=0 and +k+%2B+p=-3=>k=-3-p....eq.1
a directrix at y+=+3=>k+-+p=3=>k=3%2Bp....eq.2
from eq.1 and eq.2 we have

-3-p=3%2Bp.....solve for p
-3-3=p%2Bp
-6=2p
p=-3
go to k=3%2Bp....eq.2, plug in p
k=3-3
k=0
your equation is:
%28x-0%29%5E2+=+4%28-3%29+%28y+-+0%29
x%5E2+=+-12+y+
y=+-%281%2F12%29x%5E2++ => your answer