Answer:
Step-by-step explanation:
The vertex is halfway between focus and directrix, at (0,0).
The equation has the form y = ax².
Focal length p = distance between focus and vertex = 1
p = 1/|4a|
1 = 1/|4a|
|a| = ¼
The focus lies below the vertex, so the parabola opens downwards and a<0.
y = -¼x²
Equation represents a parabola with the focus at (0, -1) and
the directrix y=1 is [tex]x^2=-4y[/tex]
Given :
a parabola with the focus at (0, -1) and the directrix y= 1
The standard equation of parabola is [tex]y-k=\frac{1}{4p} (x-h)^2[/tex]
Focus is at (0,-1)
The midpoint of focus and directrix is the vertex
Directrix is at y=1
Midpoint of (0,-1) and y=1 is (0,0)
So the vertex is (0,0) that is our (h,k)
Now we find the value of p
The distance between vertex (0,0) and focus (0,-1) is the value of p
focus and vertex are 1 unit away. So p=-1
we got h=0 and k=0 and p=-1
Replace all the value in the standard equation
[tex]y-0=\frac{1}{4(-1)} (x-0)^2\\y=\frac{-1}{4} x^2\\4y=-x^2\\x^2=-4y[/tex]
Equation represents a parabola with the focus at (0, -1) and
the directrix y=1 is [tex]x^2=-4y[/tex]
Learn more : brainly.com/question/12582328
