what is the equation of the parabola whose focus is (-3,1) and directrix is Y=4?

Guest May 21, 2017

#1**0 **

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 - y_{1} = *a*(x - x_{1})

with *a* being found be the formula: a = 1/(4f) ---> a = 1/(4ยท1.5) ---> a = 1/6

and (x_{1}, y_{1}) being the vertex ---> x_{1} = -3 and y_{1} = 2.5.

Therefore, an equation is: y - 2.5 = (1/6)(x + 3)

geno3141
May 21, 2017