Answer:
C. (3, 0)
Step-by-step explanation:
You want to identify the point that lies on the parabola with focus (-1, 3) and directrix y = 5.
Vertex
The vertex of the parabola will lie halfway between the focus and directrix, at ...
vertex = (-1, (3 +5)/2) = (-1, 4)
Equation
The focus is below the vertex by p = 3 -4 = -1 unit, so the parabola will open downward. The equation for a parabola with vertex (h, k) and focus-vertex distance p is ...
[tex]y=\dfrac{1}{4p}(x-h)^2+k\\\\\\y=-\dfrac{1}{4}(x+1)^2+4[/tex]
Points
We know the focus (-1, 3) is not on the parabola.
The point (0, 5) is on the directrix, also not on the parabola.
The point with x=3 will give a y-value of ...
y = -1/4(3 +1)² +4 = -4 +4 = 0
The point (3, 0) is on this parabola, choice C.
