what is the equation of the parabola whose focus is (-3,1) and directrix is Y=4?
Because the directrix is a horizontal line, the parabola will be vertical.
Because the focus is below the directrix, the parabola will open downward.
The vertex of the parabola will be half-way between the focus and the directrix: vertex = (-3, 2.5)
The focal length is the distance from the focus to the vertex: focal length is: f = 1.5
An equation for a parabola is: y - y1 = a(x - x1)
with a being found be the formula: a = 1/(4f) ---> a = 1/(4·1.5) ---> a = 1/6
and (x1, y1) being the vertex ---> x1 = -3 and y1 = 2.5.
Therefore, an equation is: y - 2.5 = (1/6)(x + 3)